5.07 Radian measure of angles
State the multiplier to convert an angle from degrees to radians.
State the multiplier to convert an angle from radians to degrees.
Convert the following to radians, correct to two decimal places where applicable:
360 \degree
180 \degree
90 \degree
225 \degree
- 300 \degree
112 \degree
29 \degree
161.17 \degree
321 \degree 31 '
- 45 \degree
45 \degree
330 \degree
- 60 \degree
120 \degree
Determine whether the following statements are true or false. If it is false, correct the statement.
If 180 \degree = \pi radians, then 90 \degree must be equal to \dfrac{\pi}{2} radians.
60 \degree must be equal to \dfrac{\pi}{6} radians, because it is \dfrac{1}{6} of 360 \degree.
30 \degree must be equal to \dfrac{\pi}{3} radians, because it is half of 60 \degree.
210 \degree must be equal to \dfrac{7 \pi}{6} radians, because it is seven groups of 30 \degree.
45 \degree must be equal to \dfrac{\pi}{4} radians, because it is half of 90 \degree.
225 \degree must be equal to \dfrac{7 \pi}{4} radians, because it is seven groups of 45 \degree.
Convert the following to degrees:
\dfrac{\pi}{3}
\dfrac{\pi}{6}
\dfrac{\pi}{4}
\dfrac{3\pi}{2}
\dfrac{5\pi}{4}
-\dfrac{2 \pi}{3}
- \dfrac{5 \pi}{3}
4.2 radians
For each of the following angles:
Find the complement.
Find the supplement.
30 \degree
\dfrac{\pi}{4} radians
89 \degree 30'
\dfrac{\pi}{11} radians
Determine the quadrant of the unit circle in which the following angles lie:
2.6 radians
- \dfrac{5 \pi}{6} radians
\dfrac{ \pi}{6} radians
-6.4 radians
The graph shows a number of points on the unit circle:
Name the point that corresponds to the following angle around the circle:
\dfrac{\pi}{2} units
\pi units
-2\pi units
-\dfrac{7\pi}{4} units
The graph shows a number of points on the unit circle:
Name the point that corresponds to the following angle around the circle:
\dfrac{ \pi}{4} units
\dfrac{3 \pi}{4} units
\dfrac{21 \pi}{4} units
\dfrac{-9 \pi}{4} units
Given that \pi^{c} represents half a circle, state the fraction of the the unit circle represented by the following angles:
{\dfrac{\pi}{2}}^{c}
{\dfrac{2\pi}{3}}^{c}
{\dfrac{4 \pi}{7}}^{c}
5 \pi^{c}
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:
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:
- 2 \pi \lt \alpha \leq 0