Free Printable Unit Circle Practice

1.

Evaluate: $\sin\ \frac{\pi}{4}$

a)

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

b)

$\frac{1}{2}$

c)

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

d)

0

2.

Evaluate: $\cos\ \frac{5\pi}{6}$

a)

$-\frac{1}{2}$

b)

$\frac{1}{2}$

c)

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

d)

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

3.

Evaluate: $\sin\ \frac{7\pi}{6}$

a)

$\frac{1}{2}$

b)

$-\frac{1}{2}$

c)

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

d)

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

4.

Evaluate: $\cos\ \frac{4\pi}{3}$

a)

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

b)

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

c)

$\frac{1}{2}$

d)

$-\frac{1}{2}$

5.

Evaluate: $\sin\ \frac{2\pi}{3}$

a)

$\frac{1}{2}$

b)

$-\frac{1}{2}$

c)

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

d)

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

6.

What are the exact coordinates of $\frac{3\pi}{4}$ on the unit circle?

a)

$\left(-\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2}\right)$

b)

$\left(-\frac{\sqrt{2}}{2},-\frac{\sqrt{2}}{2}\right)$

c)

$\left(-\frac{\sqrt{3}}{2},-\frac{\sqrt{2}}{2}\right)$

d)

$\left(\frac{\sqrt{2}}{2},-\frac{\sqrt{2}}{2}\right)$

7.

Evaluate: tan (-π)

a)

undefined

b)

0

c)

1

d)

-1

8.

Evaluate: $\sin\ \frac{\pi}{6}$

a)

$\frac{1}{2}$

b)

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

c)

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

d)

2

9.

Evaluate: sin 150°

a)

$-\frac{1}{2}$

b)

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

c)

$\frac{1}{2}$

d)

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

10.

Evaluate: cos 135°

a)

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

b)

$-\frac{\sqrt{2}}{2}$

c)

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

d)

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

11.

Name the angle indicated by the graph in both radians and degrees.

a)

$-135\degree,\ -\frac{3\pi}{4}$

b)

$225\degree,\ \frac{5\pi}{4}$

c)

$-120\degree,\ -\frac{2\pi}{3}$

d)

$210\degree,\ \frac{7\pi}{6}$

12.

Name the angle indicated by the graph in both radians and degrees.

a)

$300\degree,\ \frac{5\pi}{3}$

b)

$315\degree,\ \frac{7\pi}{4}$

c)

$-60\degree,\ -\frac{\pi}{3}$

d)

$-300\degree,\ -\frac{5\pi}{3}$

13.

Evaluate:
$\cos\left(-120\degree\right)$

a)

$-\frac{1}{2}$

b)

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

c)

$\frac{1}{2}$

d)

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

14.

Evaluate:
$\cos\left(\frac{7\pi}{6}\right)$

a)

$-\frac{1}{2}$

b)

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

c)

$\frac{1}{2}$

d)

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

15.

Evaluate:
$\sin\left(-\frac{11\pi}{6}\right)$

a)

$-\frac{1}{2}$

b)

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

c)

$\frac{1}{2}$

d)

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

16.

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

a)

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

b)

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

c)

$\frac{1}{2}$

d)

1

e)

0

17.

Evaluate: $\cos\left(\frac{5\pi}{4}\right)$

a)

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

b)

$-\frac{\sqrt{2}}{2}$

c)

$-\frac{1}{2}$

d)

-1

e)

0

18.

Evaluate: $\tan\left(\frac{5\pi}{6}\right)$

a)

$-\frac{\sqrt{3}}{3}$

b)

$-\sqrt{3}$

c)

-1

d)

0

e)

does not exist

19.

Evaluate: $\sin\left(\frac{11\pi}{6}\right)$

a)

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

b)

$-\frac{\sqrt{2}}{2}$

c)

$-\frac{1}{2}$

d)

-1

e)

0

20.

Evaluate: $\cos\left(\frac{5\pi}{3}\right)$

a)

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

b)

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

c)

$\frac{1}{2}$

d)

1

e)

0

21.

Evaluate: $\tan\left(\frac{3\pi}{4}\right)$

a)

$-\frac{\sqrt{3}}{3}$

b)

$-\sqrt{3}$

c)

-1

d)

0

e)

does not exist

22.

What is the radius of a unit circle?

a)

1

b)

2

c)

$\frac{1}{2}$

d)

0

23.

What is $240\degree$ in radians?

a)

$\frac{\pi}{3}$

b)

$\frac{4\pi}{3}$

c)

$\frac{5\pi}{3}$

d)

$\frac{2\pi}{3}$

24.

What is $\frac{5\pi}{6}$ radians in degrees?

a)

$180\degree$

b)

$150\degree$

c)

$360\degree$

d)

$120\degree$

25.

In what quadrant is 285°

a)

I

b)

II

c)

III

d)

IV

26.

Which quadrant is $\frac{2\pi}{3}$ radians in?

a)

I

b)

II

c)

III

d)

IV

27.

$\sin\ \theta$ is positive in which quadrants?

a)

I and II

b)

I and III

c)

I and IV

d)

II and III

28.

What radian measure corresponds to the given point?

a)

$\frac{\pi}{4}$

b)

$\frac{3\pi}{4}$

c)

$\frac{5\pi}{4}$

d)

$\frac{7\pi}{3}$

29.

Which of these angles is in the third quadrant?

a)

$\frac{\pi}{2}$

b)

$\frac{5\pi}{3}$

c)

$\frac{4\pi}{3}$

d)

$\frac{\pi}{3}$

30.

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

a)

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

b)

$\frac{1}{2}$

c)

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

d)

$1$

31.

$\sin\left(\frac{\pi}{2}\right)=$

a)

$0$

b)

$\frac{1}{2}$

c)

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

d)

$1$

32.

$\sin\left(\frac{3\pi}{4}\right)=$

a)

$\frac{1}{2}$

b)

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

c)

$-\frac{\sqrt{2}}{2}$

d)

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

33.

$\cos\left(0\right)=$

a)

$0$

b)

$1$

c)

$-1$

d)

$\frac{1}{2}$

34.

$\cos\left(30\degree\right)=$

a)

$\frac{1}{2}$

b)

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

c)

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

d)

$1$

35.

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

a)

$\frac{1}{2}$

b)

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

c)

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

d)

$0$

36.

$\cos\left(270\degree\right)=$

a)

0

b)

1

c)

-1

d)

Undefined

37.

$\sin\left(180\degree\right)=$

a)

0

b)

1

c)

-1

d)

Undefined

38.

$\sin\left(-\frac{4\pi}{3}\right)$ =

a)

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

b)

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

c)

$\frac{1}{2}$

d)

$-\frac{1}{2}$

39.

$\sin\left(\frac{5\pi}{6}\right)=$

a)

$\frac{1}{2}$

b)

$-\frac{1}{2}$

c)

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

d)

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

40.

$\tan\left(30\degree\right)=$

a)

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

b)

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

c)

$1$

d)

$-\sqrt{3}$

41.

$\tan\left(\frac{7\pi}{4}\right)=$

a)

-1

b)

1

c)

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

d)

$-\frac{\sqrt{2}}{2}$

42.

$\tan\left(\pi\right)=$

a)

0

b)

-1

c)

1

d)

Undefined

43.

$\tan\left(\frac{3\pi}{2}\right)=$

a)

Undefined

b)

-1

c)

1

d)

0

44.

$\tan\left(\frac{4\pi}{3}\right)=$

a)

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

b)

$\sqrt{3}$

c)

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

d)

$-\sqrt{3}$

45.

$\tan\left(-210\degree\right)=$

a)

$-\frac{\sqrt{3}}{3}$

b)

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

c)

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

d)

$\frac{1}{2}$

46.

$\tan\left(-315\degree\right)=$

a)

1

b)

-1

c)

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

d)

$-\frac{\sqrt{2}}{2}$

47.

Evaluate

\sin\left(\frac{5\pi}{3}\right)

a)

$\frac{1}{2}$

b)

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

c)

$-\sqrt{3}$

48.

Evaluate

\cos\left(225\degree\right)

a)

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

b)

$-\frac{\sqrt{2}}{2}$

c)

$1$

49.

Evaluate

\tan\left(180\degree\right)

a)

$-1$

b)

$1$

c)

$0$

d)

undefined

50.

How do you feel about using the unit circle to evaluate sine, cosine, and tangent?

a)

I've got the hang of this and it's kind of fun!

b)

I've got the hang of it but I do not like it!

c)

I think I've got the hang of it, but i don't feel very confident about it.

d)

This makes little to no sense to me.

Unit Circle Practice

Total questions: 50

Worksheet time: 13hrs 30mins

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