Graphing and Shifting Trigonometric Functions
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.
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.
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.
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: