Worked example
Convert 30° to radians. Give an exact answer.
Answer & why
Answer: π/6 rad
A half turn is 180° or π radians. Multiply 30 by π/180 to get π/6 rad.
Grade 12 · Math
Convert degrees to exact radians
Express common degree angle measurements as exact multiples of π radians.
6 authored questions + worked example
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All questions
All 6 authored questions for this skill.
Question 1
Convert 60° to radians. Give an exact answer.
- π/6 rad
- 2π/3 rad
- 7π/3 rad
- π/3 rad
A hint
Multiply a degree measurement by π/180; simplify the numeric fraction.
Answer & why
Answer: π/3 rad
A half turn is 180° or π radians. Multiply 60 by π/180 to get π/3 rad.
Question 2
Convert 90° to radians. Give an exact answer.
- π rad
- π/4 rad
- 5π/2 rad
- π/2 rad
A hint
Multiply a degree measurement by π/180; simplify the numeric fraction.
Answer & why
Answer: π/2 rad
A half turn is 180° or π radians. Multiply 90 by π/180 to get π/2 rad.
Question 3
Convert 120° to radians. Give an exact answer.
- 2π/3 rad
- 4π/3 rad
- 8π/3 rad
- π/3 rad
A hint
Multiply a degree measurement by π/180; simplify the numeric fraction.
Answer & why
Answer: 2π/3 rad
A half turn is 180° or π radians. Multiply 120 by π/180 to get 2π/3 rad.
Question 4
Convert 180° to radians. Give an exact answer.
- 2π rad
- 3π rad
- π rad
- π/2 rad
A hint
Multiply a degree measurement by π/180; simplify the numeric fraction.
Answer & why
Answer: π rad
A half turn is 180° or π radians. Multiply 180 by π/180 to get π rad.
Question 5
Convert 30° to radians. Give an exact answer.
- π/6 rad
- 13π/6 rad
- π/12 rad
- π/3 rad
A hint
Multiply a degree measurement by π/180; simplify the numeric fraction.
Answer & why
Answer: π/6 rad
A half turn is 180° or π radians. Multiply 30 by π/180 to get π/6 rad.
Question 6
Convert 45° to radians. Give an exact answer.
- 9π/4 rad
- π/8 rad
- π/2 rad
- π/4 rad
A hint
Multiply a degree measurement by π/180; simplify the numeric fraction.
Answer & why
Answer: π/4 rad
A half turn is 180° or π radians. Multiply 45 by π/180 to get π/4 rad.