Trigonometry

WMA13Topic 3.23 questions

Reciprocal and inverse trig functions, compound and double angle formulae, and $R\cos(\theta \pm \alpha)$ .

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Question 15 marks
Solve, for $0 \leqslant x < 360^\circ$ ,

$\cos 2x = 3\sin x - 1$
Mark scheme
- M1 Uses $\cos 2x = 1 - 2\sin^2 x$ (1)
- A1 $2\sin^2 x + 3\sin x - 2 = 0$ (1)
Question 27 marks
(a) Express $3\cos\theta + 4\sin\theta$ in the form $R\cos(\theta - \alpha)$ , where and . Give the value of in radians to 3 decimal places.

sin2

3sinx−

M1 Solves:

(2\sin x - 1)(\sin x + 2) = 0

(1)

\sin x = \tfrac{1}{2}

, rejecting

\sin x = -2

(1)

x = 30^\circ, 150^\circ

(1)

R > 0

R > 0

R > 0

0 < \alpha < \dfrac{\pi}{2}

\alpha

(b) Hence solve, for $0 \leqslant \theta < 2\pi$ , the equation $3\cos\theta + 4\sin\theta = 2$ , giving your answers to 2 decimal places.

Mark scheme