Weekend HW!

The homework tonight was passed out at the end of class, if you weren't here or you lost it I'll post a picture below. Remember to mark all vertical asymptotes and plot all x-intercepts, then you should be able to graph the parent function using those markings.

For the critical thinking questions: (limit questions) we are just saying what is the limit of tan(x)/cot(x) approaching from the left/right and then the overall limit.

If you are having trouble look in your book! (pg 298 [tan(x)] and pg 300 [cot(x)])

BRING IN YOUR STAMPS!!!!!

Tonight's HW is just bringing in your stamps!!

STAMPS ARE DUE TOMORROW! I WILL NOT ACCEPT THEM AFTER TOMORROW!

• Count up your stamps and record the the total on the front (with your name)
• Put them in a bag or staple them together--somehow get them all together
• Double check your count! I'll randomly select 5 students to double check, and if your count is off you get a 0! (Gotta be able to count in Pre-Calc :) )

STUDY FOR TEST!!!!

Tonight's homework is just studying for the test. The template you used during class lists the four things you will need to be able to do for this test. If you are having trouble with any of those feel free to send a Remind! message, you could try doing some odd problems from the book and checking your answers in the back. Review the sequence of steps and the table for +/- cos, sin that I handed out yesterday if you're having trouble.

Topics covered on the TEST are as follows:

• Parent functions (sin, cos) and their shape
• amplitude (|a|) and how it affects graphing the parent function
• Vertical shift and how it affects graphing the parent function
• Determining Period (=2π/b) 
• For Determining equations: plug in period (into the equation above) and solve for b
• Phase shift and how it affects the parent graphs (shift the starting point (x=0) for any given function)
• Determining equations based on a graph (consider midline, amplitude, period, shape, and +/-)
• Don't worry we WILL NOT be using phase shift to determine equations only those 5!!
• Determining Equations based on written descriptions (amp of 4, shift up of 3....)
• Writing descriptions of a trig equations
• Don't forget to include the - (negative)
• a negative should be written like this "Reflected over the midline"

There is a key to last night's homework below:

5) y = -cos(2/3 x) + 2

6) y = 2sin(2/7 x) - 2

Tuesday HW/Review for TEST!

Remember to bring in STAMPs (due Wednesday!) 

• Count them, Record total on front
• Staple together, put in an envelope, create some sort of organized system to turn them in!
• DOUBLE CHECK YOUR TOTAL! (if it's wrong you'll get a 0)

#5 & 6 are below: Directions: Determine the equation to the following graph. (DO NOT CONSIDER PHASE SHIFT FOR THESE PROBLEMS! THESE GRAPHS DO NOT INCLUDE PHASE SHIFT!)
5)

 6)

*Along with the HW if you are still feeling shaky on any of the subjects below do some studying, some more extra practice!*

Here are the topics covered:

• Parent functions (sin, cos)
• amplitude (|a|) and how it affects the parent function
• Vertical shift and how it affects the parent function
• Determining Period (=2π/b) 
• (the only new thing to pay attention to when writing equations from graphs)
• plug in period (into the equation above) and solve for b
• Phase shift and how it affects the parent graphs (shift the starting point (x=0) for any given function)
• Determining equations based on a graph (consider midline, amplitude, period, shape, and +/-)
• Don't worry we WILL NOT be using phase shift to determine equations only those 5!!

A Picture of the homework is below:

Monday = Revisit/Retry the Weekend HW!

This homework assignment is out of the book! For all the problems only graph g(x), the book gives two equations f(x) and g(x) and tells you to compare, you do not need to do that, for homework just graph two periods of g(x).

Pg. 294

• 15, 16, 21, 22, 34

USE YOUR CALCULATOR OR DESMOS CALCULATOR TO CHECK IF YOUR GRAPH LOOKS CORRECT!

The book problems are below as well:

15) g(x) = sin(x - π)

16) g(x) = cos(x + π)

21) g(x) = 5 + sin(2x)

22) g(x) = -6 +cos(4x)

34) g(x) = -cos[x - (π/2)]



Also remember we have a Test Thursday! We will be reviewing on Tuesday and Wednesday so it would be a good idea to get a bit of studying in now so you can ace your classwork and be ready for Thursday!

Here are the topics covered: (notice there is something new)

• Parent functions (sin, cos)
• amplitude (|a|) and how it affects the parent function
• Vertical shift and how it affects the parent function
• Determining Period (=2π/b) 
• (the only new thing to pay attention to when writing equations from graphs)
• plug in period (into the equation above) and solve for b
• Phase shift and how it affects the parent graphs (shift the starting point (x=0) for any given function)
• Determining equations based on a graph (consider midline, amplitude, period, shape, and +/-)
• Don't worry we will not be using phase shift to determine equations only those 5

Thursday HW!

The homework tonight is the worksheet I handed out for homework. I will be posting a picture of it below if you lost it or weren't here. This homework is more than busy work its some good practice for your Quiz tomorrow. The homework covers all the same concepts so if you are able to finish this homework without a hitch you'll Ace the Quiz.

Remember: If you have any questions you can send a Remind! message. I will be here after school and free during G, H period. If you feel uncomfortable with your chances going into this test let me know, I'm here to help. 

Again, here are the topics covered:

• Parent functions (sin, cos)
• amplitude (|a|) and how it affects the parent function
• vertical shift and how it affects the parent function
• Determining Period (=2π/b) 
• (the only new thing to pay attention to when writing equations from graphs)
• plug in period (into the equation above) and solve for b
• Determining equations based on a graph (think about where the graph starts; at its min/max or mid line)

THE HOMEWORK FOR TONIGHT IN IMAGE FORMAT! (key below)

DETAILED KEY! (multiple pages long)

Wednesday HW!

Tonight's HW is just sketching one period of the graphs listed below:

• Determine b and plug it into the equation for Period
• Where should we start on the x axis? (first critical value)
• Label your last (fourth) critical value with the full period
• find half of the period for your second critical value
• take half of the second critical value to find your first critical value
• multiply the first critical value by 3 to find the third critical value

1. y = cos(x/4)
2. y = 3sin(4x)
3. y = -sin(x/3) - 1
4. y = 2cos(3x/2) + 1
5. y = -3sin( 2πx ) + 3 

We have a Quiz this Friday (and Test next Thursday) on everything about graphing that we have learned so far. This includes:

• Parent functions (sin, cos)
• amplitude (|a|) and how it affects the parent function
• vertical shift and how it affects the parent function
• Determining Period (=2π/b)
• Determining equations based on a graph (think about where the graph starts; at its min/max or mid line)

Tuesday HW!

Tonight's HW is out of the book, some practice with adjusting period.

pg. 294

• Find Amplitude & Period:  1-13 odd
• Remember Amplitude is |a| (absolute value of a)
• If you forget how to find period check your notes
• Sketch 2 Periods: 41, 42
• Take it piece by piece
1. Find critical x values (Period)
2. Consider vertical shift to determine new mid-line
3. Amplitude is simply distance from midline to max/min

I want us all to get better with homework. This is not just you, I haven't been emphasizing homework as a part of class. I plan to start class from now on with homework questions and I want nobody to be afraid to ask one. If you were having trouble on any part of the homework even something super small, voice it to the class because someone else might have had the same question and it will help you in the long run too. 

Monday HW!

Hope everyone is doing well after the weekend. Tonight's HW is out of the book, more sketching trig functions and a couple determining equations.

Pg. 294

• Determining Equations of Trig Graphs: 63-66 all
• Use max/min to find the amplitude (half the range)
• AND to find the vertical shift (mid line is midpoint of range)
• Graph two periods of the following equations: (Label max/min & vertical shift on the graph)
• y = 4 + cos(x)
• y = (-1/2) sin(x) - 1/2
• y = (1/3) sin(x) + 2

Over the Weekend!

Over the weekend the only homework is to complete that Take Home Quiz. If you were not here or lost it there are pictures of it below.

To help with your test you can check out examples from the book.

• Graphing Sin, Cos Curves (Sec 4.5): pg. 287-297
• Parent Graphs: Example 1 (pg. 288)
• Amplitude: Example 2 (pg. 289)
• Vertical Shift: Example 6 (pg. 292)
• Evaluating Trig Functions (Sec 4.2, pg 259) OR LOOK THROUGH YOUR NOTES!!!

This Quiz is an opportunity to boost your grade. The class average is depressing to say the least so this is an easy way to get a 100 in the books to boost your grade. Put in all your effort, all of you should be able to ACE this quiz, with the help of your brain and some notes. I have complete faith in every one of you. Other than that have a good weekend, play outside, relax, come in on Monday ready to overcome all these snow

days.

Thursday HW!

The homework tonight is out of the book

For all of these I want you to sketch them by hand and then verify your sketch with a graphing calculator. DO NOT use the calculator first! You'll be just wasting time instead of practicing.

pg. 294

• Sketching two graphs on the same coordinate plane: 27
• Describe differences between graphs: 17, 19 (there is only one difference in each graph)
• Sketch 2 periods: 39, 40

Monday HW!

HOMEWORK: MAKING THE DIRECTIONS FOR THE HW MORE CLEAR!!!!!!

• The ideas of amplitude and vertical shift are the same for sin and cos so just stick to one for the whole HW!
• Graph sin(x) or cos(x) parent function (in Y1)
• THEN graph your new function (multiplied by a constant or a constant added to it) (in Y2)
• Choose an "a" value based on the criteria in the question! (a greater than one, a less than -1, or an a value in between -1 and 1)
• Compare these graphs to reveal the effect of a on the graph of sin or cos
• Repeat these steps for page 2
• choose a "v" value based on the criteria (v = 0, v > 0, v < 0)
• Compare the graphs to reveal the effect of vertical shift on a graph of sin or cos
• Repeat these steps for page 3
• keep v constant throughout the page to show the effects of amplitude and vertical shift without it being too confusing
• compare the graphs to reveal how vertical shift and amplitude work together to change the graph
• Use your definitions of amplitude (1d) and vertical shift (2d) to answer the last question (3d)
• Use your graphing calculator (online calculator on the blog in links)
• If you're having trouble with this check in the book for examples
• Amplitude (pg 289)
• Vertical Shift (pg 292)

Here's a key to the classwork (including the other side that we didn't get to)

Weekend HW!

I know I didn't announce homework but as always you should be checking the blog every night! Your homework is simple tonight, you're just drawing the sin, and cos curves (just like you did in that investigation). I am providing you with a table of values, you need to draw a coordinate plane, label the x and y axes. From there just plot the points and connect them. Tomorrow we will be extending this knowledge to plot another period past the one we already drew, if you want you can brainstorm some ideas about what those x values would be for the second period. We know that the tick marks are equidistant (the same distance away), using this knowledge what can we figure out about the x values in the second period.

So, for homework this weekend: 

• Fill out a table of values for sin(x); use x-values listed below!
• Then, graph sin(x) on a coordinate plane
• Fill out a table of values for cos(x); use the x-values shown below!
• Graph cos(x) on a coordinate plane
• *Be sure to label your x and y axes correctly.
• Do this in your notes!
• You must come to class understanding how to graph these functions on Monday!
• Try to watch some youtube videos for help!
• Watch Me to Learn About Graphs of Sine and Cosine!
• Watch me too!

                            

                

X	Y = sin(x)
0
π / 2
π
3π / 2
2π

X	Y = cos(x)
0
π / 2
π
3π / 2
2π

Wednesday News!

If you did not finish that investigation yet get it done by tomorrow!
There will be an SLE tomorrow, a word problem task (based on SOHCAHTOA, and evaluating trig ratios). I will have you in "pairs" (2-3 people) working on this. It will count as a test grade so come prepared to use SOHCAHTOA and sketch triangles based on a description. There was a word problem in the back of your BINGO problems. Do that one as an example I will be posting the solution on this post below. If you need more practice there are word problems on

pg. 276

• # 57, 63 
• FIRST DO THE BINGO PROBLEM FOR PRACTICE!
  

Investigation HW (Important for Juniors)

The HW tonight is only applicable to the Juniors because they won't be in class tomorrow. Finish this investigation by Thursday. Seniors you don't have to worry we will investigate in class. The HW is posted below if you've lost your copy. Use the last page to create a table of values that you get from the investigation. (# 1,2,4,6,8) If you need a blank Unit circle there's a copy at the bottom as well.

TEST TOMORROW! (long post, just read first paragraph)

Homework tonight is to study for the Test tomorrow! If you want a quick easy way to study use that packet from Class BINGO! I have posted the answers to all the problems on the bottom of this post. For even more practice you can do some problems out of the book (again, this is a lot so just do one out of every section to make sure you know how to do everything on the Test) Below there will be a giant list of everything covered on the test, check that out make sure you know how to do it all.

Extra Practice:

• 4.1: pg. 255 #1-25 (odd) (skip 7,21), 31-51 odd, 59, 61
• 4.2: pg. 264 #5-11 odd, 23-27 odd
• 4.3: pg. 274 #5, 9-15 odd, 27,29,53,55
• 4.4: pg. 284 #3a, 5, 7, 13-16 all, 19, 21, 23, 29-35 odd, 37-43 odd, 53-65 odd

Here's a giant list of everything covered on the Test!

• Determining Quadrants given constraints
• sin (theta) > 0
• cos (theta) < 0
• Evaluating Trig Ratios/Functions... (these are the same thing)
• KNOW YOUR SPECIAL TRIANGLES!!!
• Given a coordinate point
• (3, -4)
• plot the point (connect the radius from (0,0)[the origin] to the point, create triangle from there)
• Given a trig ratio
• sin(theta) = 1/2
• tan(theta)>0
• draw reference triangle (use the ratios to find two of the side lengths and which quadrant you are in)
• Given an angle measure
• this you should be used to, graph the angle and solve
• Complement/Supplement
• Complement: The angle that intersects the terminal side of theta and 90 degrees (pi/2) 
• Supplement: The angle that intersects the terminal side of theta and 180 degrees (pi)
• Coterminals
• Angles that share a terminal position on the coordinate plane but have different angle measures (x +_ 2pi)
• Solve Triangles
• Solving unknown side length (use a trig ratio)
• Solving unknown angle (use a trig inverse)
• Convert from degrees to radians, and radians to degreees
• pi=180 degrees\

ANSWERS TO BINGO! (sqrt(2) means square root of 2

1. π/12
2. π/3
3. 277 degrees
4. -π/3
5. Quadrant 1
6. Quadrant 3
7. Quadrant 4
8. -sqrt(2)/2
9. 2sqrt(3)/3
10. Undefined
11. -2
12. -1/2
13. sqrt(3)
14. -sqrt(3)/3
15. -sqrt(3)/2
16. 300 degrees
17. 5π/4
18. -2sqrt(10)/7
19. 5sqrt(24)/24
20. -13sqrt(194)/194
21. -9sqrt(106)/106
22. 62 degrees
23. 20.21
24. 290.6 feet

HW over the weekend!

The homework over the weekend is to finish up that worksheet that I handed out at the end of class (a pdf version is available under the PDF Textbook and Assignments link section of the main page)

I would strongly suggest to use a bit of time this weekend studying for the incoming test on Tuesday, topics covered include:

• Determining Quadrants given constraints
• sin (theta) > 0
• cos (theta) < 0
• Evaluating Trig Ratios/Functions... (these are the same thing)
• KNOW YOUR SPECIAL TRIANGLES!!!
• Given a coordinate point
• (3, -4)
• plot the point (connect the radius from (0,0)[the origin] to the point, create triangle from there)
• Given a trig ratio
• sin(theta) = 1/2
• tan(theta)>0
• draw reference triangle (use the ratios to find two of the side lengths and which quadrant you are in)
• Given an angle measure
• this you should be used to, graph the angle and solve
• Complement/Supplement
• Complement: The angle that intersects the terminal side of theta and 90 degrees (pi/2) 
• Supplement: The angle that intersects the terminal side of theta and 180 degrees (pi)
• Coterminals
• Angles that share a terminal position on the coordinate plane but have different angle measures (x +_ 2pi)
• Solve Triangles
• Solving unknown side length (use a trig ratio)
• Solving unknown angle (use a trig inverse)
• Convert from degrees to radians, and radians to degreees
• pi=180 degrees

EXTRA HELP SESSION:

There's an extra help session after school on Monday, Mr. Carofano, and I will be here to help anyone who needs it, come with questions. If you are having any trouble with the problems over the weekend you should probably clear some time after school on Monday, even if its just a half hour.

MORE EXAMPLES (Review):

Here's some examples from your book: (obviously you don't have to do all of them but pick and choose and come with questions to review) 

Pg. 333 #3,5,7,9,11,13,15,17,27,29,31,41-44,45,47,49,51,57,59,67,71,73,75,77,79,781,83,85,87,89

Thursday Night HW!

The Homework is out of the book tonight, just some more practice with the stuff we've been doing. This new content is a lot like what we have seen in the beginning of the trig unit. Drawing a triangle given a ratio is just something to brush up on. Here's the homework though:

Pg. 284
# 7, 9, 13, 15, 17, 19

Something to look at if you need some help are examples 1 and 2 on pg 278-279. These are step by step problems that are the same thing we're doing in class. If you need a bit of structure look through those examples.

EXTRA HELP ON MONDAY:
We will also (as Mr. Carofano stated in class) be holding a review session after school on Monday. If you struggled with today's quiz it would be a really good idea to come to that. We will be reviewing Monday for the test as well but for extra help/practice come in after school Monday.

Wednesday (QUIZ TOMORROW)

There is no direct homework tonight, so use that time to study for your quiz instead. The quiz will not cover anything we did during class today.

The quiz will cover:

• sketch an angle (given in degrees or radians)
• evaluate the trig function (what is cos(180)?) given in degrees and radians
• label the coordinates of the special angles in the first quadrant (0, 30, 45, 60, 90)

The even problems from the HW last night are below (the answers we had on the back board today)