Free Printable Sine & Cosine Graphs Review

1.

Find the amplitude of

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

.

a)

$\frac{7}{4}$

b)

8

c)

-8

d)

$\frac{1}{8}$

2.

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

a)

a = 2, d = -1

b)

a = 2, d = 2

c)

a = 4, d = 1

d)

a = 4, d = -3

3.

Determine the period of

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

.

a)

$\frac{\pi}{3}$

b)

$\frac{1}{3}$

c)

$6\pi$

d)

$12\pi$

4.

Determine the amplitude of

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

a)

5

b)

-8

c)

-5

d)

8

5.

Determine the period and amplitude of

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

.

a)

Period: $18\pi$ ; Amplitude: 4

b)

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

c)

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

d)

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

6.

Choose the equation to represent the graph shown.

a)

$y=2\cos\left(4\theta\right)+1$

b)

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

c)

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

d)

$y=-\sin\left(2\theta\right)+1$

7.

Choose the equation to represent the graph shown.

a)

$y=2\cos\left(4\theta\right)+1$

b)

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

c)

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

d)

$y=-\sin\left(2\theta\right)+1$

8.

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.

a)

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

b)

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

c)

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

d)

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

9.

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

a)

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

b)

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

c)

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

d)

$y=\pm3\cos\left(3\theta\right)$

10.

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

Determine the amplitude of the given function.

a)

2

b)

-2

c)

4

d)

$\pi$

11.

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

Determine the vertical shift of the given function.

a)

2

b)

-2

c)

4

d)

$\pi$

12.

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

Determine the period of the given function.

a)

$2\pi$

b)

2

c)

$-\pi$

d)

$\pi$

13.

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

Determine the phase shift of the given function.

a)

$2\pi$

b)

2

c)

$-\pi$

d)

$\pi$

14.

$y=5\sin\left(6\theta+2\pi\right)-\frac{1}{2}$

Determine the amplitude of the given function.

a)

5

b)

10

c)

6

d)

2

15.

$y=5\sin\left(6\theta+2\pi\right)-\frac{1}{2}$

Determine the vertical shift of the given function.

a)

5

b)

$-\frac{\pi}{3}$

c)

$2\pi$

d)

$-\frac{1}{2}$

16.

$y=5\sin\left(6\theta+2\pi\right)-\frac{1}{2}$

Determine the period of the given function.

a)

$\frac{\pi}{3}$

b)

$-\frac{\pi}{3}$

c)

$12\pi$

d)

$6\pi$

17.

$y=5\sin\left(6\theta+2\pi\right)-\frac{1}{2}$

Determine the phase shift of the given function.

a)

$\frac{\pi}{3}$

b)

$-\frac{\pi}{3}$

c)

$12\pi$

d)

$6\pi$

Sine & Cosine Graphs Review

Total questions: 17

Worksheet time: 26mins

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