Suppose and is an angle in the third quadrant

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

Problem

Suppose tan⁡θ=724\tan\theta = \dfrac{7}{24} and θ\theta is an angle in the third quadrant. Complete the tasks below: (i) Determine sin⁡θ,  cos⁡θ\sin\theta,\;\cos\theta and sec⁡θ\sec\theta. (ii) Evaluate the numerical value of the expression E=sec⁡θ−csc⁡θE = \sec\theta - \csc\theta. (iii) Show that sec⁡2θ−tan⁡2θ=1\sec^{2}\theta - \tan^{2}\theta = 1 for this angle.

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