Trigonometry

Radians

Radians measure an angle by the length of its arc on a circle of radius 1. You need them for trigonometric functions and later for calculus.

The rules

Generated by the same engine as the Kollego course and solvable without a calculator. Pick an answer in your head, then open the solution.

1. Convert 30° to radians, expressed as a multiple of π/6. (e.g. 210° = 7·π/6, answer 7)
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Answer: 1
180° = π rad, so 30° = π/6. Divide the angle by 30 to count sixths.
30 / 30 = 1, so 30° = 1·π/6.
2. Convert 150° to radians, expressed as a multiple of π/6. (e.g. 210° = 7·π/6, answer 7)
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Answer: 5
180° = π rad, so 30° = π/6. Divide the angle by 30 to count sixths.
150 / 30 = 5, so 150° = 5·π/6.
3. Convert 60° to radians, expressed as a multiple of π/6. (e.g. 210° = 7·π/6, answer 7)
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Answer: 2
180° = π rad, so 30° = π/6. Divide the angle by 30 to count sixths.
60 / 30 = 2, so 60° = 2·π/6.
4. Convert 90° to radians, expressed as a multiple of π/6. (e.g. 210° = 7·π/6, answer 7)
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Answer: 3
180° = π rad, so 30° = π/6. Divide the angle by 30 to count sixths.
90 / 30 = 3, so 90° = 3·π/6.
5. Convert 120° to radians, expressed as a multiple of π/6. (e.g. 210° = 7·π/6, answer 7)
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Answer: 4
180° = π rad, so 30° = π/6. Divide the angle by 30 to count sixths.
120 / 30 = 4, so 120° = 4·π/6.

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