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
The diagram shows the graph of $y = \text{g}(x)$ , where

$\text{g}(x) = \arccos(x - 1) \quad \text{for } 0 \le x \le k$ (a) State the value of $k$

(1 mark)
(b) (i) On the same axes, sketch the graph of

$y = 1 + \cos x \quad \text{for } 0 \le x \le \pi$

together with the line $y = x$ for $0 \le x \le \pi$

(ii) The equation $x - 1 - \cos x = 0$ has exactly one root, $\beta$ .

Explain why $x = \beta$ also satisfies the equation

$1 + \cos x = \arccos(x - 1)$

(5 marks)
(c) Apply the Newton-Raphson method to the equation $x - 1 - \cos x = 0$ , with $x_0 = 2$ , to find $x_3$

Give $x_3$ to four decimal places.

(3 marks)
Level 4 · 9 marksTry it