1. Chapter 7/8: Sinusoidal Functions of Sine and Cosine
On the interval from 0 to 2, the graphs of the basic sine and cosine functions have five key points: the x-intercepts, the maximum, and the minimum.

2. Vertical Stretching/Shrinking of Sine and Cosine Functions
𝑌𝑜𝑢 𝑡𝑟𝑦 𝑖𝑡!
𝑦= cos 𝑥
𝑦=2 cos 𝑥
𝑦= 1 2 cos⁡(𝑥)
KEY TAKE-AWAY: x-intercepts are unchanged; multiply y-value of max/min by A (amplitude).

3. Answers to You Try It!

4. Vertical Shifting of Sine and Cosine Functions
𝑌𝑜𝑢 𝑡𝑟𝑦 𝑖𝑡!
𝑦= cos 𝑥
𝑦= cos 𝑥 +1
𝑦= cos 𝑥 −2
KEY TAKE-AWAY: If A and B remain unchanged, shift entire curve up or down.

5. Answers to You Try It!

6. Reflections of Sine and Cosine Functions
𝑌𝑜𝑢 𝑡𝑟𝑦 𝑖𝑡!
𝑦= sin 𝑥
𝑦=− 1 2 sin⁡(𝑥)
KEY TAKE-AWAY: x-intercepts are unchanged; multiply y-value of max/min by –1.

7. Answers to You Try It!

8. Horizontal Stretching/Shrinking of Sine and Cosine Functions
y = sin(x)
y = sin(2x)
What if B is not 1?

9. y = sin(x/2)
y = sin(x)
y = sin(x)
y = sin(x/3)

11. Answers to You Try It!

12. Horizontal Shifting of Sine and Cosine Functions
y = sin(x)
y = sin(x-(/3))