Free Printable Evaluating Trig. Functions using the Unit Circle

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Worksheets

Evaluating Trig. Functions using the Unit Circle

Total questions: 30

Worksheet time: 15mins

Name

Class

Date

1.

Find the exact value.

\sin\left(\frac{\pi}{4}\right)

a)

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

b)

$\frac{1}{2}$

c)

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

d)

$0$

2.

Find the exact value.

\sec\left(\frac{3\pi}{2}\right)

a)

$0$

b)

undefined

c)

1

d)

-1

3.

Find the exact value.

\cos\left(\frac{5\pi}{6}\right)

a)

$-\frac{1}{2}$

b)

$\frac{1}{2}$

c)

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

d)

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

4.

Find the exact value.

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

a)

-1

b)

1

c)

$-\sqrt{3}$

d)

undefined

5.

Find the exact value.

\cos\left(\frac{4\pi}{3}\right)

a)

$-\frac{1}{2}$

b)

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

c)

$\frac{1}{2}$

d)

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

6.

Find the exact value

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

a)

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

b)

-1

c)

1

d)

$-\sqrt{2}$

7.

Find the exact value.

\sin\left(\frac{7\pi}{6}\right)

a)

$\frac{1}{2}$

b)

$-\frac{1}{2}$

c)

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

d)

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

8.

Find the exact value.

\tan\left(-\pi\right)

a)

undefined

b)

0

c)

1

d)

-1

9.

How many degrees is ^π/₆ radians?

a)

90°

b)

60°

c)

45°

d)

30°

10.

How many degrees is ^π/₄ radians?

a)

30°

b)

45°

c)

60°

d)

90°

11.

How many degrees is ^π/₂ radians?

a)

30°

b)

45°

c)

60°

d)

90°

12.

How many degrees is ^π/₃ radians?

a)

30°

b)

45°

c)

60°

d)

90°

13.

cosθ is positive in

a)

the 1st and 2nd quadrants

b)

the 1st and 3rd quadrants

c)

the 1st and 4th quadrants

d)

the 2nd and 3rd quadrants

14.

What is the exact value of sin 150°

a)

$-\frac{1}{2}$

b)

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

c)

$\frac{1}{2}$

d)

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

15.

sinθ is positive in

a)

the 1st and 2nd quadrants

b)

the 1st and 3rd quadrants

c)

the 1st and 4th quadrants

d)

the 2nd and 3rd quadrants

16.

What radian measure corresponds to the given point?

a)

$\frac{\pi}{4}$

b)

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

c)

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

d)

$\frac{7\pi}{4}$

17.

Find the exact value.

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

a)

$-\frac{1}{2}$

b)

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

c)

$\frac{1}{2}$

d)

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

18.

$\tan\left(\theta\right)$ is positive in

a)

the 1st and 2nd quadrants

b)

the 1st and 3rd quadrants

c)

the 1st and 4th quadrants

d)

the 2nd and 3rd quadrants

19.

Find the exact value.

\csc\left(\frac{\pi}{6}\right)

a)

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

b)

$2$

c)

$\frac{1}{2}$

d)

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

20.

Find the exact value.

\csc\left(240\degree\right)

a)

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

b)

$-2$

c)

$-\frac{1}{2}$

d)

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

21.

Find the exact value.

\cot\left(540\degree\right)

a)

$0$

b)

$-1$

c)

$undefined$

d)

$1$

22.

Find the exact value.

\sec\left(120\degree\right)

a)

$-\frac{1}{2}$

b)

$-2$

c)

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

d)

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

23.

Find the exact value.

\sec\left(480\degree\right)

a)

$-\frac{1}{2}$

b)

$-2$

c)

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

d)

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

24.

Find the exact value.

\sin\left(\frac{10\pi}{3}\right)

a)

$-\frac{1}{2}$

b)

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

c)

$\frac{1}{2}$

d)

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

25.

Find the exact value.

\cos\left(690\degree\right)

a)

$-\frac{1}{2}$

b)

$\frac{1}{2}$

c)

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

d)

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

26.

a)

1

b)

0

c)

-1

d)

Undefined

27.

a)

√2

b)

√2 / 2

c)

1

d)

1 / √2

28.

a)

-√3 / 3

b)

√3

c)

-√3

d)

√3 / 3

29.

a)

-1 / 2

b)

√3 / 2

c)

-√3 / 2

d)

1 / 2

30.

a)

1

b)

-1

c)

Undefined

d)

0

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