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Standard Level

5.07 Radian measure of angles

Worksheet
Radian measure
1
a

State the multiplier to convert an angle from degrees to radians.

b

State the multiplier to convert an angle from radians to degrees.

2

Convert the following to radians, correct to two decimal places where applicable:

a

360 \degree

b

180 \degree

c

90 \degree

d

225 \degree

e

- 300 \degree

f

112 \degree

g

29 \degree

h

161.17 \degree

i

321 \degree 31 '

j

- 45 \degree

k

45 \degree

l

330 \degree

m

- 60 \degree

n

120 \degree

3

Determine whether the following statements are true or false. If it is false, correct the statement.

a

If 180 \degree = \pi radians, then 90 \degree must be equal to \dfrac{\pi}{2} radians.

b

60 \degree must be equal to \dfrac{\pi}{6} radians, because it is \dfrac{1}{6} of 360 \degree.

c

30 \degree must be equal to \dfrac{\pi}{3} radians, because it is half of 60 \degree.

d

210 \degree must be equal to \dfrac{7 \pi}{6} radians, because it is seven groups of 30 \degree.

e

45 \degree must be equal to \dfrac{\pi}{4} radians, because it is half of 90 \degree.

f

225 \degree must be equal to \dfrac{7 \pi}{4} radians, because it is seven groups of 45 \degree.

4

Convert the following to degrees:

a

\dfrac{\pi}{3}

b

\dfrac{\pi}{6}

c

\dfrac{\pi}{4}

d

\dfrac{3\pi}{2}

e

\dfrac{5\pi}{4}

f

-\dfrac{2 \pi}{3}

g

- \dfrac{5 \pi}{3}

h

4.2 radians

5

For each of the following angles:

i

Find the complement.

ii

Find the supplement.

a

30 \degree

b

\dfrac{\pi}{4} radians

c

89 \degree 30'

d

\dfrac{\pi}{11} radians

Unit circle
6

Determine the quadrant of the unit circle in which the following angles lie:

a

2.6 radians

b

- \dfrac{5 \pi}{6} radians

c

\dfrac{ \pi}{6} radians

d

-6.4 radians

7

The graph shows a number of points on the unit circle:

Name the point that corresponds to the following angle around the circle:

a

\dfrac{\pi}{2} units

b

\pi units

c

-2\pi units

d

-\dfrac{7\pi}{4} units

-1
1
x
-1
1
y
8

The graph shows a number of points on the unit circle:

Name the point that corresponds to the following angle around the circle:

a

\dfrac{ \pi}{4} units

b

\dfrac{3 \pi}{4} units

c

\dfrac{21 \pi}{4} units

d

\dfrac{-9 \pi}{4} units

-1
1
x
-1
1
y
9

Given that \pi^{c} represents half a circle, state the fraction of the the unit circle represented by the following angles:

a

{\dfrac{\pi}{2}}^{c}

b

{\dfrac{2\pi}{3}}^{c}

c

{\dfrac{4 \pi}{7}}^{c}

d

5 \pi^{c}

10

The graphs shows the unit circle divided into 12 equal segments, and a number of points on the circumference:

State two angles between - 2 \pi and 2 \pi that correspond to the following points:

a
R
b
P
c
S
d
Q
x
y
11

The graph shows a line through two points on the unit circle, A and B, and the origin, O. The line segment O B forms an angle of \theta = \dfrac{\pi}{13} with the positive x-axis. The angle between the line segment O A and the positive x-axis is \alpha.

Find the value of \alpha when:

a
0 \leq \alpha \lt 2 \pi
b

- 2 \pi \lt \alpha \leq 0

x
y
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