Break Time! Happy Holidays!

You made it! Have an awesome break! Rest up, relax, spend some quality time with family and friends, and come back recharged for our midterm exams!

There is no formal assignment to complete over winter vacation. However, it would be a very good idea to start studying for your midterm! You will have some review assignments after break, so some studying would make those assignments a little easier!

There will not be any more stamp problems for this quarter, so it would also be a good idea to count up your stamps and get them together! They'll be due on exam day (or before).

Lastly, here's what's going on the two days after break (with the sub):

• Monday: You should be given a "packet" (2 pages) with "Graphing Review!" as the title. You should complete as much of this in class as possible (hopefully all of it), and complete the rest for homework. This must be completed for Thursday, January 7th.
• Tuesday: You will be given another packet, this time multiple choice. This says "Universal Screen: Trigonometry." Again, complete what you can in class, and complete the rest for homework. Skip questions 20 and 21. 
• Ultimately, you need to have both packets completed and with you in class on Thursday.
• Be productive! Make yourself (and me) proud! Convince me that I made the right decision in not giving you break work by doing a great job with the sub!

See you all in 2016! Enjoy your time off!

Almost there...

No homework tonight!

However, if you did not finish your test today, you will have the opportunity to do so tomorrow! So study, study, study if there was anything you didn't know how to do!

Check yesterday's blog post for more info about the test (if you need it)! Otherwise, see you tomorrow!

Enjoy your Tuesday!

TST TMRW!

STUDY, STUDY, STUDY! Test tomorrow!

Tomorrow's test will cover identities (sections 5.1 and 5.2) and solving trig equations (section 5.3).

• You will be given a blank unit circle
• 3 forms of the Pythagorean identities will be provided
• The best way you can study is to complete the review multiple choice questions provided in class, and review today's stamp problem!

Here's an outline of exactly what's on the test tomorrow:

• Simplify/verify trig identities
• Using Pythagorean identities
• With factoring
• "Diamond method/style" (if there's 3 terms)
• Factor out a greatest common factor (GCF)
• Difference of squares (2 terms)
• Adding/subtracting fractions
• Find a common denominator and simplify
• "Foiling"
• Remember, (a + b)^2 IS NOT equal to a^2 + b^2 (We have to "foil," so we'd get a^2 + 2ab + b^2)
• Solving trig equations
• Isolate/solve for the trig term (get it "by itself")
• Taking square roots (remember the + or -)
• Combining like terms
• Substituting using Pythagorean identities
• Factoring, "quadratic or diamond method/style" (3 terms)
• Move all terms to one side and then factor

Lastly, here are the multiple choice answers so you can use them to study!

Weekend = Study for Tuesday!

We have a test on Tuesday covering sections 5.1, 5.2, and 5.3--in other words, our test will be entirely made up of identities and trig equations!

On Monday we will review for our test....it would be a good idea to start studying this weekend since you don't have any official homework!

• Use the bingo questions/answers I gave you today--do these practice problems to get ready for the "solving trig equations" part of the test!
• Look over your identities quizzes!
• Look at the examples (maybe even write them down to help you remember) from sections 5.1, 5.2, and 5.3 of your test!

See you Monday! Then, test Tuesday, and a little trig Weds! 

Have a great weekend!

Thursday HW!

Tonight, please complete the 7 trig equations that we started in class (or below): (and do it so we can play bingo tomorrow!)

• If you were out, do these 7 problems and you'll be all caught up! They're based on Wednesday's notes!

Thursday HW

Tonight, please complete the 2 problems provided in class (or below):

Both of these problems will require you to factor "quadratic style"! Good luck!

Only 4.5 more days of hard work! Tomorrow we'll continue working with quadratic like trig equations, Friday we'll review our trig equations, Monday we'll get ready for our test, and then it's test time on Tuesday! Stay focused and do your homework!

Great work yesterday in class, and getting Monday night's homework done!

Tuesday HW

Tonight, please complete any (quiz) questions that you did not finish in today's class. Remember, this is a quiz, so get these done!

• If you have less than 4 problems left to do then just do the ones you didn't finish!
• If you're checking the blog you can finish any problems you didn't finish in class! (even if it's more than 4)!
• If you were absent today, complete each of the 9 problems below on separate paper (number each problem, write the equation, show all work) and you'll be all caught up!

See you all tomorrow--for some different (harder?) trig equations! Almost there!

Want some extra credit toward your quiz grade? (This extra credit can boost any past quiz if you get over a 100% on this)!

• You can get one point for trying each, and then additional points if you solve them correctly!
• Extra credit: solve each of these additional equations: both will require you to use Pythagorean identities and combine like terms...

Monday HW!

Tonight, please solve the 7 trig equations that we started in class (or below).

• Remember, for 1-4 you want to move all of the trig terms to one side, then factor, then solve (find the angle measures that satisfy the equation)
• For 5-7, isolate the trig term (get it by itself), then find the angle measures that satisfy the equation

Tomorrow in class we'll have a graded assignment based on tonight's homework. You will have to do this by yourself tomorrow--so do your homework! Then, we'll learn how to solve "quadratic like" trig equations.

Here's an outline of what's coming up until break:

• Tuesday: classwork (individual, graded); notes on solving "quadratic like" trig equations
• Wednesday: more notes/practice with "quadratic like" trig equations
• Thursday: classwork--solving trig equations (all types)
• Friday: solving trig equations bingo!
• Monday: review of identities and solving trig equations (for test)
• Tuesday: test on identities and solving trig equations (5.1 to 5.3)
• Wednesday (half day): quick midterm review assignment

Weekend HW: Only 2 Problems!

This weekend, please complete the following in your textbook:

Page 364: 21, 24

For each of these problems you'll have to use the same strategy as we did in class today--move the terms to one side of the equation, then factor.

I plan to check this Monday--should be easy homework credit since it's only 2 problems! So do it!

Have a great weekend! 7.5 more school days until break!

Thursday HW: Solving Trig Equations

Tonight, please complete the following in your textbook: (THIS HOMEWORK WILL COUNT AS DOUBLE, SO DO IT!)

Page 364: 1, 7, 13, 17, 18, 19

• SHOW ALL WORK! If you do not, then you copied the answers from the back of the book....that's a 0!
• Remember, when you are asked to "verify," you need to substitute the given angle measure into the equation and show that it is a solution
• Use our notes from today for solving the equations! If you get stuck, look at the examples on pages 356-357!
• If you do not do question 18 then you can receive at most half credit!

See you tomorrow for some more trig equations!

No HW!

No homework tonight! Enjoy your night off!

Tomorrow we'll get back to work on solving trig equations! See you there!

VERIFYING IDENTITIES QUIZ TOMORROW!

Tomorrow you will have 25 minutes for your "verifying identities" quiz! Study!

• Look over the "Things to Look For" sheet I made and gave to you!
• Review the problems from Friday's quiz (that you got back today)!
• Look back at last night's homework examples, as well as today's classwork!
• Google stuff! (verifying identities)
• Be sure you know how to use a conjugate to verify an identities
• Also be sure you can find a common denominator when adding/subtracting fractions
• Make sure you know how to FACTOR to verify...
• With 3 terms, use the "diamond method" type factoring...(     )(     )
• With 2 terms, remember to look for a difference of squares!

Monday HW!

Monday = back to the grind! Time to work!

Tonight, please complete the "Verifying Trig Identities Quiz" provided in class (or below).

Also, remember that ALL MAKEUP HOMEWORK/QUIZZES MUST BE COMPLETED BY WEDNESDAY (or after school Weds.)!

Tomorrow in class we will work together to practice some verifying identities! Then, on Wednesday, we'll take a verifying quiz, and then begin some new stuff!

See you there!

Here are the 6 homework questions in case you need them:

Weekend HW = Collected and Graded (so do it!)

This weekend, please complete the "Solving Trig Equations" worksheet provided in class (or below).

This assignment will be collected and graded as classwork, so make sure you get it done! (That means it weighs a lot more than a "regular" homework!)

Use section 5.3 of your book for help, or maybe check out some of the links on the right! You got this! And make sure you try the bonus!

Here are some examples you can use as a reference: this weekend's homework takes us back to the unit circle, with a little bit of a "new" twist...

Have a great weekend and I'll see you all on Monday for some more identities!

Identities Quiz Tomorrow!

Tomorrow we will start class with our quiz on trig identities! You will have a max of 25 minutes for the quiz! (After that, we'll get into more verifying...)

We all know these identities are hard...so it's important that you STUDY!

• Look over the take home quiz answer key I gave you! Read through these examples and the solutions! It would be a great idea to re-try the take home quiz on your own, then use my answer key to check your work!
• Review the "8 Basic Trig Identities" worksheet we had for homework!
• You also have an answer key for this! Read through the solutions and see what you did right/wrong!
• Read over the "Things to Look For" sheet I gave you today in class! These are general tips we can use for solving identities!
• KNOW YOUR IDENTITIES! Be sure you know the Pythagorean identities and the other basic reciprocal/quotient identities (our notecards)!
• Look in section 5.1 and 5.2 of your textbook to see more examples done out!
• Look up videos online about trig identities (simplifying and verifying)!
• THE ONLY WAY TO GET BETTER AT IDENTITIES IS TO PRACTICE!

See you tomorrow! Enjoy your Thursday!

Wed nes day HW

Tonight please complete the following problems from your textbook (remember, I gave you a printout of the page in class today, so you may not need your book):

Page 346: 33, 37, 51, 53, 61, 63, 65

• Remember to pay attention to the words I boxed or notes I made by the questions--these are giving you hints as to how to start each identity!
• Good luck! Remember--it's all about trying!

And here are the answers so you can check:

33.) 1

37.) 1 + sinY

51.) cos^2(x) ("cosine squared x")
53.) cosx + 2

61.) 1 + 2sinxcosx

63.) tan^2(x) ("tan squared x")

65.) 2csc^2(x) ("2 cosecant squared x")

Two'sDay HW

Tonight, please complete the trig identities worksheet provided in class today! (the problems are below if you lost yours or were out)

Remember...trig identities are about a few things:

1. Practice. Each problem is different; the only way to get better is to do tons of practice problems, so do your homework!
2. SHOWING WORK. Your work is what's being graded, so your work must be organized, neat, and thorough to receive full credit.
3. Trying. Because each problem is different, you may not know what to do immediately. Identities (and "real math") are about trying different strategies/ideas; some may work, others may not. If you try something and it leads to a dead end, try something else.

Welcome back! Quiz Tomorrow!

Welcome back! I hope you all had an awesome break of resting, relaxing, and lots of eating!

I'm looking forward to getting back to work tomorrow! Be ready to work hard as we continue to push through these trigonometric identities for about another week, with some quizzes along the way.

Tomorrow we will start class with a quiz: write/derive the Pythagorean identities in at least 5 different ways/forms! You'll have about 7 minutes to do this. Whether you memorize the identities or understand how to derive them, that's up to you--but get an A tomorrow!

If you were out today you missed the STAR test; you will have to make it up! (Classwork grade)

After our quiz we'll get into some more practice! See you there! Have a great Monday!

Happy Thanksgiving!

Enjoy your break! Rest up, relax, enjoy some time with friends and family, and be ready for lots of intense math when you return!

Over break, please be sure to complete your trig identities take home quiz (DUE MONDAY)!

• Remember, it's your work that I'm looking at when I grade these...so be neat and organized, and show all work!
• In the answer bank you will use option E (secX) twice and you will use option S (1) twice. 
• All of the other options will be used once.
• DO NOT FORGET TO GET THIS DONE--IT'S A QUIZ GRADE!

Also, remember that we have the STAR test on MONDAY (11/30) AFTER BREAK in the LIBRARY MATH CPU LAB! 

I will still be collecting your take home quizzes Monday, so don't forget!

Have an awesome break! See you in a few days!

Here's the take home quiz:

Monday HW

Tonight, please complete the following in your textbook (I'm checking!) These problems are on the printed copy I gave you in class, so you may not need your book:

Page 345: 15-18 (eliminate matching options c and e), 21-25 (eliminate matching option D)

Weekend HW

This weekend, please complete the "Introduction to Trigonometric Identities" worksheet provided in class (or below)! 

I'm definitely checking!

Have a great weekend and I'll see you all on Monday!

Thursday HW

Tonight, please complete the "Trig Identities and Algebra" worksheet provided in class!

Make sure you do it! I'm checking! AND, this is the foundation for the math we'll be doing moving forward, so start strong!

See you all tomorrow for some more identities!

Here's the homework in case you lost it or were absent!

No homework tonight!

How are you feeling about today's test? Hopefully confident! I'm looking forward to grading them and seeing lots of A's!

Tomorrow we get into some intense math with trigonometric identities; we'll start by reviewing a variety of algebraic strategies, including factoring, "foiling" or multiplying polynomials, and finding common denominators. See you there!

Have a great Wednesday!

Test Tomorrow!

Tomorrow we have our first test of the second quarter! STUDY! This will have a major impact on your class average!

Here's an outline of what's on the test!

• 10 multiple choice questions
• Study the 10 pre-test questions we discussed in class today! (Same questions with different numbers tomorrow!)

• Open Ended:
• Graph sine/cosine with vertical shifts, changes to period, amplitude, and reflections
• Write equation of a sine/cosine function given the graph
• Write equation of a sine/cosine function given a description
• Know how to find x-intercepts/asymptotes for tan(x), cot(x), sec(x), csc(x)
• Evaluating inverses (like tonight's homework)
• There are some true/false questions dealing with...
• Asymptotes
• X-Intercepts
• Domain
• Range
• Study the trig functions summary table from the weekend!
• Graph arcsin(x), arccos(x), and arctan(x)
• You will have to graph one of these three functions on the test!

Monday HW and Test Weds!

Tonight, please complete the 16 "Evaluating Inverses" problems provided in class (or below).

Tomorrow we'll wrap up our discussion/notes and do some review to get ready for Wednesday's test!

Start studying now! Here's an outline of what's on the test!

• 10 multiple choice questions
• Study the 10 pre-test questions we discuss in class tomorrow! (Same questions with different numbers on Weds!)
• Open Ended:
• Graph sine/cosine with vertical shifts, changes to period, amplitude, and reflections
• Write equation of a sine/cosine function given the graph
• Write equation of a sine/cosine function given a description
• Know how to find x-intercepts/asymptotes for tan(x), cot(x), sec(x), csc(x)
• Evaluating inverses (like tonight's homework)
• There are some true/false questions dealing with...
• Asymptotes
• X-Intercepts
• Domain
• Range
• Study the trig functions summary table from the weekend!
• Graph arcsin(x), arccos(x), and arctan(x)
• You will have to graph one of these three functions on the test!

Weekend HW!

This weekend, please complete the summary table for the 6 trig functions (provided in class or below). This is a great way to start studying for Wednesday's test!

• THERE IS A MISTAKE IN THE TABLE I GAVE YOU! The asymptotes that were given for tan(x) are incorrect! (I actually wrote the asymptotes for cot(x)
• Pay attention to the functions at the top!
• I just did mine mindlessly and graphed my functions in the wrong places and had to re-do it!

Test Wednesday:

• Graphing sine and cosine with changes to amplitude, period, reflections, and vertical shifts (section 4.5)
• Know how to graph (like Thursday's sub work)
• Know how to write equations given a graph or description of a function
• Know how to calculate amplitude, period, identify shifts/reflections
• Graphing the quotient and reciprocal functions (4.6)
• Know how to graph tan(x), cot(x), sec(x), csc(x)
• Know which functions have the same asymptotes or x-intercepts and why
• Study the "critical thinking questions" we discussed in class!
• Evaluating trig inverses with a restricted domain (4.7)
• Graphing inverses
• Know how to graph arcsin(x), arccos(x), and arctan(x) and determine the domain restrictions
• Evaluate compositions of inverses (4.7)

Here's your homework in case you lost it!

Back to Inverses Tomorrow!

I'm sorry that I was not there with you today! I plan to do my best to have perfect attendance (other than my honeymoon) from here on out so we can do our best to prepare ourselves for our exams, and more importantly, so we can learn lots of trig!

Today's classwork is a great opportunity to review for our unit test, and will be graded (our first classwork grade of the quarter). Do your best!

I look forward to getting back to work and graphing arctan(x) and arccos(x) tomorrow! See you there!

Tuesday/Wednesday HW

Tonight/tomorrow, please complete the "Evaluating Inverses" worksheet provided in class.

Use the 3 examples at the top for help! If these aren't enough, take a look at the examples in section 4.7 of your textbook, or use some of the resources (links) on the right!

I'll definitely be checking this homework on Wednesday!

Here's an outline of what's coming up in PreCalc:

• Wednesday: Graph arccos(x) and arctan(x)
• Thursday: More evaluating inverses!
• Friday: Evaluating/graphing practice (classwork)
• Monday: Section 4.7 wrap up: evaluating and graphing inverses and compositions
• Tuesday: Review for test (everything from 4.5, 4.6, 4.7)
• Wednesday 11/18: TEST ON GRAPHING AND INVERSES
• Thursday/Friday: Intro to our new unit, trig identities!

Quiz Tomorrow = Homework due Thursday!

Tomorrow we will start class with a quick, 15 minute quiz! Here's what's on it:

• Graph y = tan(x)
• Graph y = cot(x)
• Graph y = sec(x)
• Graph y = csc(x)
• There will also be 2 of the "critical thinking" questions where you have to write explanations (we went over these in class...)
• For example, "Which function has the same asymptotes as tangent? Explain why." Or, "Which functions do not have x-intercepts? Explain why."

No Thursday HW!

No homework tonight! Enjoy your night off!

Tomorrow we'll complete a table summarizing the graphs and properties of the 6 trig functions (sine, cosine, tangent, cotangent, secant, cosecant).

Then, we'll get back to practicing some trig inverses! Yay!

Have a happy Thursday!

Wednesday HW

Tonight, please complete the "Reciprocal Graph Wrap Up" worksheet provided in class.

• Each answer will be sine, cosine, tangent, cotangent, secant, or cosecant, along with an explanation of WHY.
• This is our first homework grade for the second quarter, so I'm definitely checking and it counts as double!

Tomorrow in class we'll go over these (quickly), and then move on to our "new stuff," section 4.7! Woohoo!

Here are the homework questions in case you lost yours or were out:

Take Home Quiz Due Weds!

Please complete the "Evaluating Trig Ratios" worksheet that I passed out today!

• This will be collected and graded as a take home quiz on Wednesday!

• YOU MUST SHOW WORK to receive full credit
• If you simply hand in a bunch of circled answers with no work, you can at best score a 50%!

Use your notes and get an A! Start off the second quarter strong!

In case you lost your paper, here are the questions! Enjoy! See you all on Wednesday!

Last Chance for Extra Credit!

Happy Halloween and Happy Homecoming! Have a blast this weekend! Have fun, hang out with friends and family, and be safe!

This weekend you have no "official" homework. However, here is your last extra credit assignment/opportunity for the quarter:

Page 333: 27, 31, 49-52, 85, 89

• Complete these on separate paper and turn them in on Monday to boost your first quarter grade!

After you do your extra credit, rest up, relax, and be ready to graph cotangent, cosecant, and secant on Monday!

Oh, and be sure to listen to these tomorrow!

Stamps Due Tomorrow!

Your only homework tonight is to get your stamps together--they're due tomorrow!

Stamps due tomorrow!

• Count up your stamps (double check!)
• Staple them together/put them in an envelope/bag, and write the total on the front!
• If the total on your paper does not match your actual total you'll get a 0! Double check!
• Stamps must be turned in by Friday!
• You're literally counting the number of blue ladybug stamps you have! 

Once you're stamps are ready (or if you've already turned them in), enjoy you Thursday without homework!

If you'd like to get a head start, the "evaluating trig ratios" review worksheet below is due Monday! And it's the first homework grade of the second quarter, so I'm definitely checking, and I'm counting it as double!

• **you MUST SHOW WORK on the homework to receive full credit! If you're homework is just a bunch of circled answers with no work, you will earn a 0!**
• Feel free to show your work on separate paper!

No HW = Count Your Stamps!

No homework tonight! Tomorrow we'll get started on our next section, graphing tangent, cotangent, secant, and cosecant...it's going to get crazy!

Since there's no homework, tonight is a good night to get your stamps together!

Remember, stamps are due this week (by Friday)!

• Count up your stamps (double check!)
• Staple them together/put them in an envelope/bag, and write the total on the front!
• If the total on your paper does not match your actual total you'll get a 0! Double check!
• Stamps must be turned in by Friday!
• You're literally counting the number of blue ladybug stamps you have! 

"Quest" Tomorrow, Extra Credit Opportunity Below!

STUDY! 

Tomorrow we will have our "quest" on graphing sine and cosine. Here's what's on it:

• There are 3 problems where you have to graph a given trig function (sine or cosine)
• Remember to look for any vertical shifts and draw a new midline
• Then, use the a value to determine the amplitude, and draw dotted lines for the max and min values
• Next, we find the period (2pi/b!), and use this to label the key points on our x axis
• Finally, sketch the function!
• The shape depends on whether this is a sine or cosine graph
• Also, pay attention to any negatives to see if the graph is reflected!
• This is the same stuff that was on your take home quiz!
• For one of the three graphs, you are asked to graph two periods (you can add a second positive period, or a negative one, you're choice)
• Next, you are given a description of a function, and asked to write the equation
• For example: "Write the equation of a cosine graph that is not reflected, has a period of 6pi, an amplitude of 3, and is shifted 4 units down."
• You have to describe two differences between the graphs of sin(x) and cos(x)
• Next, you have three problems where you are given a graph and asked to write the equation
• We discussed this and have examples from Monday!
• First, find the midline (remember, midline = (max + min)/2
• Next, use the midline to determine the amplitude
• OR, amplitude = (max - min)/2
• Third, we have to use the period to solve for b
• Remember, period = 2pi/b
• OR, remember that b represents "the number of complete cycles between 0 and 2pi," so it is possible to find b by looking at the graph!
• Finally, determine if you have a sine or cosine graph and whether or not it's reflected (-)
• Write your equation!
• Finally, you have two questions where you are given a function and asked to describe any reflections, determine the amplitude, find the period, and describe any shifts
• For example, if I gave the function y = -4sin(2x) +1
• Amplitude = 4 (look at the "a," and remember amp. is always positive)
• Reflected? yes (because of the negative)
• Shifted: "up 1" (because of the +1)
• Period = 2pi/b = 2pi/2 = pi
• Study our stamp problem from today!

If you'd like to get some extra credit on your test grade, complete the 3 problems that were written on the board (or below) on separate paper. The number of extra points you earn will depend on whether your answers are correct or incorrect. So, do these on separate paper and bring them tomorrow for some extra test points!

Good luck studying! Check out the blog post from Friday for some videos that can help with graphing! 

And lastly...Remember, stamps are due this week (by Friday)!

• Count up your stamps (double check!)
• Staple them together/put them in an envelope/bag, and write the total on the front!
• If the total on your paper does not match your actual total you'll get a 0! Double check!
• Stamps must be turned in by Friday!
• You're literally counting the number of blue ladybug stamps you have! 

Monday HW

Tonight, please complete the 4 graphs provided in class (or below)!

Tomorrow we'll wrap up this unit and get ready for our "quest" on Wednesday!

Also, remember, stamps are due this week!

• Count up your stamps (double check!)
• Staple them together/put them in an envelope/bag, and write the total on the front!
• If the total on your paper does not match your actual total you'll get a 0! Double check!
• Stamps must be turned in by Friday!
• You're literally counting the number of blue ladybug stamps you have! 

HW = Take Home Quiz!

This weekend, please complete the classwork we started today in class. Remember you can skip questions 7 and 8. This will be collected and graded on Monday as a 31 point take home quiz! 

YOU WILL LOSE 5 POINTS FOR EVERY DAY THIS IS LATE. NO PAPERS WILL BE ACCEPTED AFTER WEDNESDAY. NO EXCUSES!

We will have a quiz/test (quest?) on this same stuff on Wednesday! So, if you put in lots of effort on your take home quiz, not only will you get a better grade, but you'll be better prepared for your "quest!"

• When I'm grading the graphs, I'm looking for 5 pieces (each @ 1 point):
• Period (so show the work on the side!)
• X Axis labeled
• Correct vertical shift (midline)
• Correct amplitude (show dotted lines for max/min values)
• Correct shape (pay attention to if it's sine or cosine, and if the graph is reflected)
• For question 3...
• First solve for b: you know the period is "3pi," so 2pi/b = 3pi. Then, cross multiply to solve for b!
• Remember, it tells you this is a cosine graph!
• This is reflected--how do we show that in the equation?
• The amplitude is 7--where do we see that in the equation?
• And lastly, there is a vertical shift "9 down"--how do we see this in the equation?
• Try questions 7 and 8! You can get up to 4 extra credit points for each!
• To write these equations (we'll talk about this Monday), FIRST, find the midline
• Remember, the midline is halfway between the max and min!
• This gives us our "d"
• Then, find the period--how long does it take to complete one cycle of the graph?
• Once we determine the period, set up an equation to solve for b (like the first bullet for question 3 above)
• Next, consider the amplitude and if the graph is reflected to determine the "a" value
• Lastly, decide if this is a sine or cosine graph!
• Write your equation!
• You got this!

Here are the questions you need to do (in case you lost yours). Use axes like the ones below for each of your 5 graphs.

Feel free to email with questions! Also, check out some videos on youtube for help with graphing! I provided some helpful links below! And most importantly, USE YOUR NOTES!

Check out these videos for help!

Graphing Trig Functions (Period, Amplitude)

Graphing Trig Functions with Vertical Shifts!

Thursday HW

Tonight you have the shortest homework assignment ever...

Please graph the following function: 

y = 3sin4x - 4

Tomorrow we'll do some classwork/practice with graphing vertical shifts! See you there!

Enjoy your long afternoon!

Wednesday HW, Pop Quiz Tomorrow

We will start class with a 2 question pop quiz tomorrow. You are given two equations and asked to graph each. (You will be labeling your own axes like last nights homework/answer key, not like today's classwork). 

Tonight, please complete the worksheet provided in class (or below).

• Match each equation (1-12) to the twelve graphs below.
• If you fill in the letter of each graph that matches to each number (at the bottom), you'll find the hilarious answer to the question (joke?) at the top of the paper! Sweet!
• Math wise, think about the following...
• Sine or Cosine? This will immediately narrow down the options.
• Then, think about the amplitude to narrow your choices down further
• Finally, use the period (2pi/b!) to determine which graph is which!
• Personally, I'd look at the equations and then think about the graph...but you could definitely start from the graph and work backward to the equation--whatever works for you!

2s Day HW

Tonight, please complete the 6 graphs on the worksheet we started in class!

The equations are below (for those of you who were out or lost yours...):

• Graph each equation on axes (like those shown)
• Label the y axis
• Label the x axis (quarter period, half period, three-quarter period, and full period) with 4 values
• Sketch the graph!

Tomorrow we'll get back to work and write some more equations....then, we'll have to start moving our graphs up/down/left/right, and then we'll be ready for a graphing test! Yay!

See you all tomorrow! Nice work today!

Monday HW

Did you ace the quiz today? I hope so! You should have them back (or at least in the grade book) by tomorrow...

Tonight, please complete the following for homework:

Page 294: 1, 3, 5, 7, 9, 11, 13

Remember, amplitude is determined by "a," the coefficient to our trig function. And to find the period, we must find "2pi divided by b," where b is the coefficient to x.

Tomorrow we'll continue to practice with graphing, and start to move our functions up/down/left/right! Wooo!

Study, study, study, study!

Study, study, study, study, study, study, study....and have a great weekend!

On Monday we will start class with a quiz--the quiz is (literally) the same as the "Sine and Cosine Parent Functions: Maxima, Minima, and Intercepts" worksheet we went over in class today!

So, on your quiz, you'll have to...

• Graph two periods of sine and cosine
• For each graph/function:
• Identify domain (all possible x values, or "left to right") and range (all possible y values, or "bottom to top") 
• Define the x values of all maxima
• Define the x values of all minima
• Define the x values for all x-intercepts/zeroes 
• The quiz is worth 30 points! Get an A!

Also, remember that if you fully complete the worksheet provided in class (4.5 Math Lab: Graphing Periodic Functions) (which is a review of all the stuff on your quiz!) and show me on Monday you'll get a few extra points added to your quiz!

• Of course you have all the answers to this worksheet, but try it as a quiz! 
• If you can do this paper without any notes you'll be ready to get an A on Monday's quiz!

Enjoy your weekend and I'll see you all Monday!

Check out this video Joseph told me about....we have a bunch of salt on a surface and sound is being used to make the salt form different shapes! The different types of sound (waves) all make the salt move differently!

Extra Credit HW!

Get some extra credit tonight!

Complete BOTH SIDES of the notes sheet we started today in class!

• For cosine, try to identify ALL maxima, minima, and intercepts
• Then, for sine...
• Provide the domain/range and max/min values (of y)
• Identify all maxima, minima, and intercepts

Tomorrow in class we'll go over all of this before we start transforming our graphs of sine and cosine!

See you all tomorrow!

STUDY, STUDY, STUDY!

Unit 4 Multiple Choice test (retake) tomorrow! 15-20 minutes when the bell rings!

Tonight, study! Look over the 10 pre-test questions that I gave you in class last week (or below). Remember, tomorrow's test is the same questions with different numbers! Study, study, study!

• You will have 15-20 minutes to complete the 10 multiple choice. Study so you know what you're doing! 
• This will count as a (4th) test grade for this quarter for everyone, regardless of the first test score! Get an A+!
• Prepare yourself to do well and take advantage of this opportunity!

Lastly, here are the answers to the "pre-test" so you can check your work, along with some explanations!

1. B (Remember, complements have to sum/add to 90 degrees, or pi/2 radians...so we need to subtract the angle measure given from pi/2--which requires a common denominator. OR, since you have a calculator, convert everything to degrees to find the answer (remember, pi = 180 degrees). So, this angle = 180/10, or 18 degrees; so the supplement must be 72 degrees! We can then convert each answer to degrees to see which one matches!)
2. D (For this question, mark each of the axes with the angle measures. For instance, we know pi/2 will be 7.5pi/15. We know pi = 15pi/15, and we know 2pi = 30pi/15. We can then use these as references to figure out which quadrant the terminal side falls in.) (OR, maybe it helps to convert the angle to degrees--plug in 180 for pi! So we can do -31x180/5 to find this angle in degrees, then determine the quadrant!)
3. B (Unit circle! This question is simply asking for the coordinate pair for this angle. Draw the angle, then use special triangles to find the x/y coordinates.) (OR, think about this...let's focus on the x coordinate...we know the x coordinate is cosine. So let's type cos(-240) in our calculator--make sure it's degree mode!. If we enter cos(-240) we get -1/2, so we know the xcoordinate has to be -1/2! So the answer must be B!)
4. B (This is a weird question...I would start  by looking at which sides (a,b,c) are used, and which angle they focus on. In this question, we're focusing on the 45 degrees (our theta), and we're using sides a (opposite) and b (adjacent). If we're using opposite and adjacent, this must be tangent!)
5. B (Remember these word problems? You were good at them! To start, draw a triangle; label the angle measure and side length given. Also label the side you're looking for with a variable. Now, decide which trig ratio you have to use--in this question, we're given the hypotenuse (ladder), and trying to find the opposite side--so we'll have to use sine. We know sin(62)=x/20! Set up the equation, cross multiply, and solve!) (Also, think about this...we know the hypotenuse, the longest side, is 20, so the answer must be less than 20--so we can at least narrow it down to two answers!)
6. B (This is straight from our most recent notes! Either use A/S/T/C (All student take calc) OR think about the x and y coordinates to determine where each inequality is true! Remember, >0 means positive, and <0 means negative.)
7. B (Again, straight from our most recent notes. For this question, first determine which quadrant the angle falls in (like #6). Then, draw a triangle in this quadrant, labeling your reference angle as theta.) (OR, think about this...they give us tangent, so that's the "opposite over adjacent." So we know the adjacent side is 5...this question asks us for cosine, which is "adjacent over hypotenuse," so we know the numerator = adjacent = 5. The answer must be B or D. Then, since tangent is negative and sine is negative, we must be in quadrant 4--in quadrant 4, cosine is positive, so the answer is B!)
8. D (More from our most recent notes! Plot the point; then, draw a triangle to the x axis. Label two sides of the triangle using the coordinates. Then, label your reference angle as theta. Now, use SOHCAHTOA to find the indicated ratio!)
9. A (Start by labeling each axis with the appropriate angle measures, but in radians "as decimals." For example, we know pi = 3.14 and 2pi = 6.28. For this question, remember we're looking at a negative angle, so -pi/2 = -1.57 (the bottom of the y-axis). The top of the y axis, or -3pi/2 = -4.71. We can then use these four points as a guide--which two values does our angle fall between? This will help us find which quadrant the angle falls in. For this question, -3.4 falls between -3.14 and -4.71, so this must be in quadrant 2. Then, for the reference angle, we'll take 3.4 - 3.14!)
10. D (Back to the unit circle! First, sketch the angle in standard position. Then, use your unit circle to find the coordinates OR draw a triangle formed with the x-axis, and label the sides using special triangles. Then, we have to think about our ratio--in this case, cotangent = x/y, so we take our x value divided by our y-value!) (Here's another way: make sure your calculator is in degree mode, and then enter 1/tan(-390). Write down this decimal. Then, convert each multiple choice option to a decimal to see which one matches!)

Tuesday HW

Tonight, please graph the parent function for y = cos(x) !

• Create a table values (just like we did today for sin(x))
• Label your x axis (radians) and y axis (-1 to 1)
• Plot your points
• Sketch the cosine function!

When you're done, your graphs should look like this!

4 Day Weekend and TAKE HOME TEST!

Also, this weekend, please complete the TAKE HOME TEST provided in class (or below)!

• This is a test grade! Use your notes, your textbook, and any online resources you like to help you get a 100%! Take advantage of the "take home" part of the test!
• Questions 1-10 will be the test grade....questions 11-14 are extra credit!
• TRY THE EXTRA CREDIT! Don't waste a chance at extra points! Nothing happens if they're wrong!
• For questions 10-14, you're thinking backwards...
• Remember, an "inverse" is used to find an angle....so you have to think backwards with your unit circle, and determine what angles have the given ratio
• For example, #11 is asking you "which angles on the unit circle have a sine that is -root 2 over 2?"
• Or #12 asks, "which angles on the unit circle have a cosine equal to one half?"
• 11-14 should each have 2 answers

The take home test shouldn't take toooo long....get it done early, and then enjoy the rest of your week! The take home test is below if you need it!

TEST TOMORROW!

Study, study, study, study, study, study, study! You have to know what you're doing in order to have time to finish!

Use the 14 homework problems (assigned Monday) to study the "new stuff" from section 4.4!

Page 284: 7, 9, 13, 15, 19, 21, 29, 31, 45, 49, 51, 55, 63, 65

Also, you definitely want to study your unit circle--you will be given a blank unit circle, which you can fill out and then use on your test! (You don't have to, it's up to you)!

You'll also want to review your "evaluating trig ratios" stuff...we had our classwork from Friday (in groups, graded out of 24) you can look at. You also have a "Trig Functions and the Unit Circle: Quiz" handout that we did for homework--I gave you an answer key that has all of the solutions/work shown.

Those are the three best tools you have to study!

Here's an outline of EXACTLY what's on your test:

Open Ended Section: NO graphing/scientific CALCULATOR!

• Define each of the 6 trig ratios in terms of x and y
• Determine which quadrant an angle falls in, given ratios are +/-
• Ex: If cosA>0 and cotA<0, which quadrant does angle A fall in?
• Ex: p. 284 #13-16
• Sketch angles in standard position (both radians and degrees)
• Find the exact value (evaluate) of trig ratios 
• look at the "Trig Functions and the Unit Circle: Quiz" worksheet or Friday's groupwork (graded out of 24).
• Ex: p. 285 53-66, 29-36
• Given a ratio and the sign (+/-) of another ratio, evaluate the 6 trig functions 
• Ex: p. 284 #19, 21
• Given a coordinate point, plot the point, draw a triangle, and find the 6 trig ratios
• Ex: p. 284 #5, 7, 9, 11

Multiple Choice Section: Graphing/Scientific CALCULATOR ALLOWED

• Look at the 10 "pre-test" questions I gave you today in class...tomorrow's multiple choice questions are the same types, just different numbers! (and even in the same order)

Lastly, here are the answers to the "pre-test" so you can check your work!

1. B
2. D
3. B
4. B
5. B
6. B
7. B
8. D
9. A
10. D

Tuesday HW

Please complete the following in your textbook--these problems will be checked Thursday!

Page 284: 7, 9, 13, 15, 19, 21, 29, 31, 45, 49, 51, 55, 63, 65

This is an excellent way to review for our test on Thursday! Study, study, study, study, study!

Monday/Tuesday HW

Please complete the following in your textbook--these problems will be checked on Wednesday!

Page 284: 7, 9, 13, 15, 19, 21, 29, 31, 45, 49, 51, 55, 63, 65

Do your homework = studying for our test Wednesday!

Tomorrow/Weds. I'll post more info about our test!

Tomorrow we'll finish our notes on 4.4 in class, and then on Wednesday we'll do some in-class practice/review for the test Thurs!

Have a great Monday!

Weekend HW (Sorry)

This weekend, please complete the (sideways) worksheet provided in class.

• For the top section, each answer should be +, -, or neither
• For the bottom section, your job is to choose the letter (from the coordinate pairs around the circle) that represents each ratio...
• For example, #18) cos180 would be represented by point i

The homework is also below if you need it!

Great work today in class everyone! I'm looking forward to grading this stuff--I'm hoping for lots of A's!

Your homework shouldn't take too long; get it done, and then enjoy the rest of your weekend!

We'll finish up with some new stuff on Monday and Tuesday, and then use Wednesday to get ready for our test!

Extra Credit HW and Quiz Tomorrow!

Tonight, STUDY STUDY STUDY!

Want some extra credit? You can get rid of a past homework 0 if you do these problems!

Page 264: 5 -12 (For each angle measure find the coordinates on the unit circle).

This homework will be some built in studying for your quiz!

Remember, tomorrow's quiz = I give you a unit circle, you have 13 minutes (ish) to fill it out completely! You WILL be timed, so study, study, study!

WinsDay Homework

Tonight, please complete the "Trig Functions and the Unit Circle: Quiz" worksheet that we started in class!

Tomorrow we'll get back to the unit circle and keep practicing!

Don't forget, QUIZ FRIDAY--I give you a blank unit circle, you fill it out!

See you tomorrow!

2sDay HW

Tonight, please complete the following in your textbook: 

page 264: 21, 29, 31, 33, 35

Don't have your book? Here are the problems! :)

21.) Find sine, cosine, and tangent: theta = -3pi/2

Evaluate each:

29.) sin(5pi)

31.) cos(8pi/3)

33.) cos(-13pi/6)

35.) sin(-9pi/4)

Monday HW!

Back to work with this unit circle thing tomorrow!

Tonight, please complete the (blank) unit circle provided in class! 

• Label all angle measures in radians!
• Label all angle measures in degrees!
• Label the coordinates for each point on the unit circle!

**I know you can easily look these answers up online, or in the textbook. However, we will have a quiz (in a couple days) where you are given the same unit circle, and you have to fill it out on your own! If you do this independently tonight, you'll be ready for the quiz! If you simply look up the answers, you won't be prepared for the quiz!

Weekend HW: Investigate!

This weekend, please complete the "Sine, Cosine, and Tangent Investigation" provided in class.

• Just as you developed the unit circle on your own, this homework pushes you to "figure out" some of the new stuff we'll discuss next week!
• The more time/effort you put into (successfully) completing this and understanding it, the easier your upcoming week will be!
• Check below for some help if you get stuck!
• Questions 3-8 are dependent upon you finishing #2--if you're stumped, use my copy of the homework  below (with notes/hints) to help!

Good luck! This investigation will DEFINITELY be checked (as homework) on Monday! We'll jump right into our new notes--we'll review how to make that unit circle, and then start to evaluate trig functions on the unit circle!

Enjoy your weekend! Hope you aced our test today!

Homework (Investigation) Hints:

• **You may have to save the picture (if you're using a computer) to zoom in more

Homework Questions (Blank Worksheet):