An angle satisfies with

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

Problem

An angle θ\theta satisfies sec⁡θ=−43\sec\theta = -\dfrac{4}{3} with π<θ<3π2\pi < \theta < \dfrac{3\pi}{2}. Work through the following steps: (i) Determine cos⁡θ\cos\theta and state its sign. (ii) Using the value of cos⁡θ\cos\theta, find sin⁡θ\sin\theta. (iii) Compute tan⁡θ\tan\theta and cot⁡θ\cot\theta. (iv) Show numerically that tan⁡θ⋅cot⁡θ=1\tan\theta \cdot \cot\theta = 1 for your values.

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