Sine & Cosine Graphs Review

Find the amplitude of

 $y=-8\cos\left(\frac{7x}{4}\right)$  .

•  $\frac{7}{4}$  

• 8

• -8

•  $\frac{1}{8}$  

Find a and d for the function f(x) = asinx + d such that the graph of f(x) matches the graph shown.

• a = 2, d = -1

• a = 2, d = 2

• a = 4, d = 1

• a = 4, d = -3

Determine the period of

 $y=3\cos\left(\frac{x}{6}\right)-5$  .

•  $\frac{\pi}{3}$  

•  $\frac{1}{3}$  

•  $6\pi$  

•  $12\pi$  

Determine the amplitude of

 $y=-8\cos\left(\frac{\pi\theta}{16}\right)-5$  

• 5

• -8

• -5

• 8

Determine the period and amplitude of

 $y=4\cos\left(\frac{x}{9}+\frac{\pi}{6}\right)$  .

• Period:  $18\pi$  ; Amplitude: 4

• Period:  $\frac{\pi}{9}$  ; Amplitude: 4

• Period:  $-\frac{2\pi}{9}$  ; Amplitude: -4

• Period:  $\frac{2\pi}{9}$  ; Amplitude: 4

Choose the equation to represent the graph shown.

• $y=2\cos\left(4\theta\right)+1$

• $y=-\sin\left(\frac{1}{2}\theta\right)+1$

• $y=4\cos\left(\frac{1}{2}\theta\right)+1$

• $y=-\sin\left(2\theta\right)+1$

Choose the equation to represent the graph shown.

• $y=2\cos\left(4\theta\right)+1$

• $y=-\sin\left(\frac{1}{2}\theta\right)+1$

• $y=4\cos\left(\frac{1}{2}\theta\right)+1$

• $y=-\sin\left(2\theta\right)+1$

Write the equation for a sine function with a reflection over the x-axis, period of

 $\pi$  , a phase shift of  $\frac{\pi}{2}$  , and a vertical shift of 4.

•  $y=-\sin\left(2\theta-\pi\right)+4$  

•  $y=-\sin\left(x-\frac{\pi}{2}\right)+4$  

•  $y=-\sin\left(2\theta+\pi\right)+4$  

•  $y=-\sin\left(x+\frac{\pi}{2}\right)+4$  

Write the equation for a cosine function with an amplitude of 3 and a phase shift of  $-\frac{\pi}{3}$  .

•  $y=\pm3\cos\left(\theta+\frac{\pi}{3}\right)$  

•  $y=\pm3\cos\left(\theta-\frac{\pi}{3}\right)$  

•  $y=\pm3\cos\left(\frac{\theta}{3}\right)$  

•  $y=\pm3\cos\left(3\theta\right)$  

 $y=-2\cos\left(\theta+\pi\right)-2$  

Determine the amplitude of the given function.

• 2

• -2

• 4

•  $\pi$