For an angle in the second quadrant it is given that

MATHEMATICS · Multi-part · AP · AP Precalculus · Trigonometric and Polar Functions · Trigonometric and Polar Functions

Problem

For an angle θ\theta in the second quadrant it is given that sec⁡θ+tan⁡θ=−2\sec\theta + \tan\theta = -2. Answer the following: (i) Prove that sec⁡θ−tan⁡θ=−12\sec\theta - \tan\theta = -\dfrac{1}{2}. (ii) Hence find the exact values of sec⁡θ\sec\theta and tan⁡θ\tan\theta. (iii) Using the results of part (ii), determine sin⁡θ,  cos⁡θ,  csc⁡θ\sin\theta,\;\cos\theta,\;\csc\theta and cot⁡θ\cot\theta. (iv) Confirm that sin⁡2θ+cos⁡2θ=1\sin^{2}\theta + \cos^{2}\theta = 1 for the obtained values.

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