Mathematics

Mathematics

Problem

For an angle θ\theta, it is given that sin⁡θ=513\sin\theta = \dfrac{5}{13} and θ\theta lies in the second quadrant. a. (i) Find cos⁡θ\cos\theta. b. (ii) Hence determine tan⁡θ\tan\theta and sec⁡θ\sec\theta. c. (iii) Evaluate S=sin⁡2θ+cos⁡2θ+tan⁡2θS = \sin^{2}\theta + \cos^{2}\theta + \tan^{2}\theta and write the answer as a single rational number.

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