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.

Start practising Read the lesson

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

DifficultyAll Level 2 Level 3

1
Solve $\sec x = 2$ for $0 \le x \le 2\pi$ , giving your answers as exact multiples of $\pi$ .
Level 3 · 2 marksTry it
2
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
3
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
4
Solve $\cot x = -1$ for $0 \le x \le 2\pi$ , giving your answers as exact multiples of $\pi$ .
Level 3 · 2 marksTry it
5
(a) State the range of $y = \operatorname{cosec} x$ .
(b) Hence state the number of solutions of $\operatorname{cosec} x = 0.5$ in the interval $0 \le x \le 2\pi$ .
Level 3 · 2 marksTry it

3 more questions on reciprocal trigonometric functions

Free with an account — just an email, no card. The whole bank, every mark scheme and worked solution.

Start free