Free Printable Core Graphing Sine and Cosine

1.

What is the amplitude of

$y=-3\sin\left(7x\right)-2$ ?

2.

What is the period of

$y=4\cos\left(5x\right)$ ?

3.

What is the period of

y=-3\sin\left(x\right)

?

a)

π

b)

2π

c)

3π

d)

4π

4.

The period of a sine or cosine graph can be found by ....

a)

It's always $2π$

b)

$\frac{2π}{B}$

c)

$B\cdot2π$

d)

$2π+B$

5.

What is the amplitude of

$y=4-2\cos3\left(x-\frac{π}{2}\right)$

6.

What is the amplitude?

7.

$y=4\cos\left(2x\right)$ is graphed above.
What number would go in the
🔹 ?

8.

$y=4\cos\left(2x\right)$ is graphed above.
What number would go in the 🔸 ?

9.

$y=4\cos\left(2x\right)$ is graphed above.
What number would go in the

⚫️ ?

10.

$y=4\cos\left(2x\right)$ is graphed above.
What number would go in the 🌕

?

a)

π

b)

2π

c)

$\frac{π}{4}$

d)

4π

e)

$\frac{π}{2}$

11.

Write the equation

a)

$y=-3\sin\left(\frac{1}{2}x\right)$

b)

$y=3\sin\left(\frac{1}{2}x\right)$

c)

$y=-3\sin\left(2x\right)$

d)

$y=3\sin\left(2x\right)$

e)

$y=-3\sin\left(\frac{π}{2}x\right)$

12.

Which of the following is true?

a)

$y=-2\cos x$ has a y-intercept of (0,-2)

b)

$y=\cos\left(x\right)$ is an ODD function

c)

$y=2\cos x$ has a domain of [-2,2]

d)

$y=-3\sin\left(x\right)$ has a y-intercept of (0,-3)

e)

$y=\sin\left(x\right)\$ has an x-intercept at $\left(\frac{π}{2},0\right)$

13.

What is the range of

y=-7\cos\left(3x\right)

a)

[-7,7]

b)

(-∞,∞)

c)

[-3,3]

d)

[-2π,2π]

e)

$\left[\frac{-3}{7},\frac{3}{7}\right]$

14.

What is the period of

$y=4\cos\left(\frac{π}{2}x\right)$
Type pi for π if necesssary

15.

$y=2\cos\left(2x\right)+2$
describe any stretch or compression from the graph of $y=\cos\left(x\right)$

a)

vertical stretch by a factor of 2 and a horizontal compression by a factor of $\frac{1}{2}$

b)

vertical stretch by a factor of 2 and a horizontal stretch by a factor of 2

c)

vertical compression by a factor of $\frac{1}{2}$ and a horizontal compression by a factor of $\frac{1}{2}$

d)

vertical compression by a factor of $\frac{1}{2}$ and a horizontal stretch by a factor of 2

16.

The period of a graph is 16. What would be the B value in the equation: $y=A\sin B\left(x-h\right)+k$

a)

16

b)

16π

c)

$\frac{π}{8}$

d)

$\frac{1}{8}$

e)

8π

17.

What is the period of the graph above?

18.

What is the equation of the graph above?

a)

$y=-2\cos\left(\frac{π}{3}x\right)$

b)

$y=-2\cos\left(\frac{π}{6}x\right)$

c)

$y=-2\cos\left(12x\right)$

d)

$y=-2\cos\left(6x\right)$

e)

$y=-2\cos\left(\frac{1}{3}x\right)$

19.

What is the amplitude of the graph?

a)

1

b)

3

c)

2π

d)

$\frac{5π}{2}$

e)

$\frac{5}{2}$

20.

What is the equation of the blue graph?

a)

y = 2sin x

b)

y = sin(2x)

c)

y = sin(x + 2)

d)

y = sin(x) - 2

e)

y = sin(x - 2)

21.

Half of the height from max to min

a)

amplitude

b)

period

c)

symmetry

d)

coterminal

e)

quadrantal

22.

Number of units to complete one wave or cycle

a)

period

b)

quadrantal

c)

amplitude

d)

terminal side

e)

coterminal

23.

$\cos\left(\frac{\pi}{4}\right)$

a)

$\frac{1}{2}$

b)

$\frac{1}{\sqrt{2}}$

c)

$\frac{1}{\sqrt{3}}$

d)

$\frac{\sqrt{3}}{2}$

e)

$\sqrt{3}$

24.

$\tan\left(\frac{\pi}{3}\right)$

a)

$\frac{1}{2}$

b)

$\frac{1}{\sqrt{2}}$

c)

$\frac{1}{\sqrt{3}}$

d)

$\frac{\sqrt{3}}{2}$

e)

$\sqrt{3}$

25.

$\frac{π}{2}$ radians = _________°

26.

$\sin\left(\frac{\pi}{3}\right)$

a)

$\frac{1}{2}$

b)

$\frac{1}{\sqrt{2}}$

c)

$\frac{1}{\sqrt{3}}$

d)

$\frac{\sqrt{3}}{2}$

e)

$\sqrt{3}$

27.

$\tan\left(\frac{\pi}{6}\right)$

a)

$\frac{1}{2}$

b)

$\frac{1}{\sqrt{2}}$

c)

$\frac{1}{\sqrt{3}}$

d)

$\frac{\sqrt{3}}{2}$

e)

$\sqrt{3}$

28.

$\sin\left(\frac{\pi}{6}\right)$

Do NOT enter a decimal

29.

$\frac{π}{4}$ radians = _________°

30.

$\frac{π}{3}$ radians = _________°

31.

$\frac{π}{6}$ radians = _________°

32.

Find the acute angle $\theta$ , such that $\cos\theta=\frac{1}{2}$ .

a)

$\frac{\pi}{2}$

b)

$\frac{\pi}{3}$

c)

$\frac{\pi}{4}$

d)

$\frac{\pi}{6}$

33.

Find the acute angle $\theta$ , such that $\tan\theta=\sqrt{3}$ .

ANSWER IN RADIANS Type pi for π if needed

a)

$\frac{\pi}{3}$

b)

$\frac{\pi}{4}$

c)

$\frac{\pi}{6}$

d)

$\frac{\pi}{2}$

34.

Find the acute angle $\theta$ , such that $\tan\theta=1$ .

a)

$\frac{\pi}{4}$

b)

$\frac{\pi}{6}$

c)

$\frac{\pi}{3}$

d)

$\frac{\pi}{2}$

35.

Find the angle $\theta$ , such that $\sin\theta=1$ .

ANSWER IN RADIANS

36.

Find the angle $\theta$ , such that $\cos\theta=-1$ .

a)

π/2

b)

π/6

c)

π/3

d)

π/4

e)

π

Core Graphing Sine and Cosine

Total questions: 36

Worksheet time: 51mins

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