Welcome to PreCalculus! Use this blog to stay up to date on homework, upcoming quizzes/tests, and other class news! Also, explore the variety of resources to help you in your PreCalc endeavors!
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!
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!**
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!
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!
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!
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!
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!
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....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!
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!
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!)
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!)
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!)
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!)
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!)
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.)
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!)
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!)
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!)
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!)
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!
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
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!
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!
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!
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!
