# Graphing and Shifting Trigonometric Functions

#### Instructions:

Your initial post will include **five screen shots **and **four sentences** (one sentence for each of the last four screen shots).

##### Screenshot #1

- Flip a coin. Your flip will determine the trigonometric function you will be working with for your initial post.
- Heads = use
*sine* - Tails = use
*cosine* - For example, if I flipped a tail, my initial post would focus on the trigonometric function cosine.
- Graph your function and take a screen shot of the graph.
- You can use any program you like. Here is one option: Illuminations: Trigonometric Graphing.
- Please refer to the discussion board on how to take screen shots.
- Graph
y=cos(x)

or

y=sin(x)

- Your subject line will be cos(x) or sin(x) depending on your flip.

##### Screenshot #2

- Now, consider this equation.
*The equation used will depend on your original coin toss.*y=Acos(B(x−C))+D

y=Asin(B(x−C))+D

- Using the Illuminations: Trigonometric Graphing site, figure out what happens when you make
*A*larger (try 1, 2, 3, and 4).

- Explain in one sentence what happens as you make
*A*larger and tell us what this transformation is called. - Then pick an interesting large number (something larger than 1), and graph
y=Acos(x)

or

y=Asin(x)

*The equation used will depend on your original coin toss.* *Take a screen shot of your graph and post the equation.*

*Screenshot #3*

*Using the Illuminations: Trigonometric Graphing site, figure out what happens when you make**B*larger (try 1, 2, 3, and 4) and tell us what this transformation is called.- Explain in one sentence what happens as you make
*B*larger. - Then pick an interesting large number (something larger than 1), and graph
y=cos(Bx)

or

y=sin(Bx)

*The equation used will depend on your original coin toss.* *Take a screen shot of your graph and post the equation.*

- Explain in one sentence what happens as you make

*Screenshot #4*

*Screenshot #4*

*Using the Illuminations: Trigonometric Graphing site, figure out what happens when you make**C*larger (try 0, 30 degrees, 45 degrees, and 60 degrees) and tell us what this transformation is called.- Explain in one sentence what happens as you make
*C*larger. - Then pick an interesting large number (something larger than 0), and graph
y=cos(x+C)

y=sin(x+C)

*The equation used will depend on your original coin toss.* - Take a screen shot of your graph and post the equation.

- Explain in one sentence what happens as you make

*Screenshot #5*

*Screenshot #5*

*Using the Illuminations: Trigonometric Graphing site, figure out what happens when you make**D*larger (try 0, 1, 2, and 3) and tell us what this transformation is called.- Explain in one sentence what happens as you make
*D*larger - Then pick an interesting large number (something larger than 0), and graph
y=cos(x)+D

or

y=sin(x)+D

*The equation used will depend on your original coin toss.* *Take a screen shot of your graph and post the equation.*

- Explain in one sentence what happens as you make

*Response Post:*

*Response Post:**Pick another student’s post who flipped their coin opposite of you.*- For my example, I would pick someone who flipped heads, or has sin(x) in their subject line.

*Review the other student’s post.*- Does each of their answers make sense to you?
- Explain in at least two sentences why or why not their post makes sense.
- Please be respectful of other students’ work.

*Pick two of their transformations (meaning A, B, C, or D and the corresponding graph).*- What happens when you change the transformation from a positive value to a negative value? For example, if you picked A and D, what happens when you change equations to:
y=−Acos(x)

or

y=−Asin(x)

**Remember, find the Trig function opposite of yours.** - What happens when you change the equation to:
y=cos(x)−D

or

y=sin(x)−D

- Post a screen shot of both transformations together:
y=−Acos(x)−D

or

y=−Asin(x)−D

- What happens when you change the transformation from a positive value to a negative value? For example, if you picked A and D, what happens when you change equations to: