A Level

MATHEMATICS · Multi-part · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Let sin⁡θ=35\sin\theta=\dfrac{3}{5} where π2<θ<π\dfrac{\pi}{2}<\theta<\pi. (i) Calculate cos⁡θ\cos\theta and tan⁡θ\tan\theta. (ii) Find sin⁡2θ\sin 2\theta, cos⁡2θ\cos 2\theta and tan⁡2θ\tan 2\theta. (iii) Hence compute the value of sin⁡2θ+cos⁡2θtan⁡2θ\dfrac{\sin 2\theta+\cos 2\theta}{\tan 2\theta}, simplifying your answer.

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