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.

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).

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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.

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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.

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

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

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