A-level · Trigonometry

Inverse trigonometric functionsExam-style questions

The functions arcsin, arccos and arctan — why the domains of sin, cos and tan must be restricted to invert them, the principal ranges, and evaluating exact values and composite expressions.

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

DifficultyAll Level 2 Level 3 Level 4

1
State the domain and range of (a) $\arcsin x$ ,
(b) $\arccos x$ ,
(c) $\arctan x$ .
Level 2 · 3 marksTry it
2
Find, in radians, the exact values of (a) $\arcsin\frac{1}{2}$ ,
(b) $\arccos 0$ ,
(c) $\arctan\sqrt{3}$ .
Level 2 · 3 marksTry it
3
(a) State the range of $\arctan x$ .
(b) Explain why $\arctan x$ is defined for every real number $x$ , whereas $\arcsin x$ is not.
Level 2 · 2 marksTry it
4
Find, in radians, the exact values of (a) $\arccos\!\left(-\frac{1}{2}\right)$ ,
(b) $\arcsin\!\left(-\frac{\sqrt{2}}{2}\right)$ ,
(c) $\arctan(-1)$ .
Level 3 · 3 marksTry it
5
Find the exact value of $\arcsin\!\left(\sin\frac{2\pi}{3}\right)$ .
Level 3 · 2 marksTry it

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