For an acute angle we have

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

Problem

For an acute angle θ\theta we have tan⁡θ=512\tan\theta = \dfrac{5}{12}. Answer the following. (i) Find sec⁡θ\sec\theta. (ii) Hence calculate cos⁡θ\cos\theta correct to three decimal places. (iii) Using the values obtained, verify numerically that sin⁡2θ+cos⁡2θ=1\sin^{2}\theta + \cos^{2}\theta = 1. Take sin⁡θ=513\sin\theta = \dfrac{5}{13} for your verification.

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