Let be an angle such that and .

MATHEMATICS · Multi-part · CBSE · Mathematics · Trigonometric Functions · Trigonometric Functions

Problem

Let θ\theta be an angle such that sin⁡θ=35\sin \theta = \dfrac{3}{5} and π2<θ<π\dfrac{\pi}{2} < \theta < \pi. (i) Find cos⁡θ\cos \theta. (ii) Determine tan⁡θ\tan \theta. (iii) Evaluate sin⁡2 ⁣θ+cos⁡2 ⁣θ\sin^{2}\!\theta + \cos^{2}\!\theta. (iv) Hence compute 1−2sin⁡2 ⁣θ1 - 2\sin^{2}\!\theta.

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