A-level · Differentiation

Differentiating trigonometric functionsExam-style questions

How fast a sine or cosine is changing. Why the gradient of sin x traces out cos x; proving it from first principles with the small-angle results; why x must be in radians; the other four derivatives from the quotient rule, and the minus every co-function carries; the chain rule on sin kx and sin²x; and using trig derivatives for rates, tangents and stationary points.

Start practising Read the lesson

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

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
$\text{f}(x) = x\cos x + 2 \qquad 0 \leqslant x \leqslant \pi$

where $x$ is measured in radians.
(a) Find $\text{f}'(x)$

(2 marks)

The curve with equation $y = \text{f}(x)$ has a maximum turning point at $x = \alpha$
(b) Show that $\alpha$ lies in the interval $[0.8, 0.9]$

(2 marks)
(c) Using $x_0 = 0.8$ as a first approximation for $\alpha$ , apply the Newton–Raphson method once to $\text{f}'(x)$ to find a second approximation for $\alpha$ , giving your answer to 3 decimal places.

(3 marks)
Level 4 · 7 marksTry it