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.

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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
A curve has equation $y = 4\sin^{2}x\cos x$ for $0 < x < \tfrac{1}{2}\pi$ .

Find the $x$ -coordinate of the stationary point of the curve. Give your answer correct to 3 significant figures.

(3 marks)
Level 2 · 3 marksTry it
2
Differentiate $y = \tan(2x)$ .
Level 2 · 2 marksTry it
3
Differentiate $y = \cos(5x)$ .
Level 2 · 2 marksTry it
4
Differentiate $y = \sin(3x^2)$ .
Level 2 · 2 marksTry it
5
Differentiate $y = \sin 4x + \cos 2x$ . (2 marks)
Level 2 · 2 marksTry it

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