# 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
1. Flip a coin. Your flip will determine the trigonometric function you will be working with for your initial post.
• Tails = use cosine
• For example, if I flipped a tail, my initial post would focus on the trigonometric function cosine.
2. 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
1. 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

2. Using the Illuminations: Trigonometric Graphing site, figure out what happens when you make larger (try 1, 2, 3, and 4).
1. Explain in one sentence what happens as you make A larger and tell us what this transformation is called.
2. 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.

3. Take a screen shot of your graph and post the equation.
##### Screenshot #3
1. Using the Illuminations: Trigonometric Graphing site, figure out what happens when you make larger (try 1, 2, 3, and 4) and tell us what this transformation is called.
1. Explain in one sentence what happens as you make B larger.
2. 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.

3. Take a screen shot of your graph and post the equation.

##### Screenshot #4
1. Using the Illuminations: Trigonometric Graphing site, figure out what happens when you make larger (try 0, 30 degrees, 45 degrees, and 60 degrees) and tell us what this transformation is called.
1. Explain in one sentence what happens as you make C larger.
2. 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.

3. Take a screen shot of your graph and post the equation.

##### Screenshot #5
1. Using the Illuminations: Trigonometric Graphing site, figure out what happens when you make larger (try 0, 1, 2, and 3) and tell us what this transformation is called.
1. Explain in one sentence what happens as you make D larger
2. 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.

3. Take a screen shot of your graph and post the equation.

##### Response Post:
1. 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.

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

3. Pick two of their transformations (meaning A, B, C, or D and the corresponding graph).
1. 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.

2. What happens when you change the equation to:

y=cos(x)−D

or

y=sin(x)−D

3. Post a screen shot of both transformations together:

y=−Acos(x)−D

or

y=−Asin(x)−D