Suppose is an angle such that and .

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

Problem

Suppose θ\theta is an angle such that sin⁡θ>0\sin\theta>0 and cos⁡θ<0\cos\theta<0. (i) Identify the quadrant in which θ\theta lies. (ii) Determine the signs of sec⁡θ\sec\theta and csc⁡θ\csc\theta separately. (iii) Show that the product sec⁡θ csc⁡θ\sec\theta\,\csc\theta must be negative for every such θ\theta. (iv) Is it possible for sec⁡θ csc⁡θ=0\sec\theta\,\csc\theta=0 for any real θ\theta? Give reasons for your answer.

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