A-level · Trigonometry

Radian measureExam-style questions

What a radian is, converting between degrees and radians, the exact values at the special angles in radians, and solving trigonometric equations over an interval given in radians.

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10 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3

1
(a) Express $150^\circ$ and $225^\circ$ in radians, giving each answer as an exact multiple of $\pi$ .
(b) Express $\frac{7\pi}{12}$ radians in degrees.
Level 2 · 3 marksTry it
2
Solve $2\cos x = \sqrt{3}$ for $0 \le x \le 2\pi$ , giving your answers as exact multiples of $\pi$ .
Level 2 · 3 marksTry it
3
Without using a calculator, find the exact value of (a) $\cos\frac{5\pi}{6}$ ,
(b) $\sin\frac{3\pi}{4}$ ,
(c) $\tan\frac{7\pi}{6}$ .
Level 2 · 3 marksTry it
4
Solve $\sqrt{2}\,\sin x + 1 = 0$ for $0 \le x \le 2\pi$ , giving your answers as exact multiples of $\pi$ .
Level 3 · 3 marksTry it
5
Solve $\cos 2x = -\frac{1}{2}$ for $0 \le x \le 2\pi$ , giving your answers as exact multiples of $\pi$ .
Level 3 · 4 marksTry it

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