A-level · Trigonometry

Reciprocal trigonometric functionsExam-style questions

The three reciprocal functions secant, cosecant and cotangent — their definitions, the shape and key features of their graphs, exact values, and solving equations that involve them.

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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
Find the exact values of (a) $\sec\frac{\pi}{4}$ ,
(b) $\operatorname{cosec}\frac{2\pi}{3}$ ,
(c) $\cot\frac{5\pi}{6}$ .
Level 2 · 3 marksTry it
2
Find the exact values of (a) $\sec\pi$ ,
(b) $\operatorname{cosec}\frac{\pi}{2}$ ,
(c) $\cot\frac{\pi}{3}$ .
Level 2 · 3 marksTry it
3
Solve $\sec x = 2$ for $0 \le x \le 2\pi$ , giving your answers as exact multiples of $\pi$ .
Level 3 · 2 marksTry it
4
Solve $\operatorname{cosec} x = -2$ for $0 \le x \le 2\pi$ , giving your answers as exact multiples of $\pi$ .
Level 3 · 2 marksTry it
5
Solve $\cot x = \sqrt{3}$ for $0 \le x \le 2\pi$ , giving your answers as exact multiples of $\pi$ .
Level 3 · 2 marksTry it

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