Answer the following questions related to reciprocal trigonometric ratios.

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

Problem

Answer the following questions related to reciprocal trigonometric ratios. (i) State the reciprocal identities that relate sin⁡θ\sin\theta, cos⁡θ\cos\theta and tan⁡θ\tan\theta with their respective reciprocals. (ii) Using a right–angled triangle, explain why sin⁡θ csc⁡θ=1\sin\theta\,\csc\theta = 1 for any acute angle θ\theta. (iii) If sin⁡θ=513\sin\theta = \dfrac{5}{13} for an acute angle θ\theta, interpret geometrically what csc⁡θ\csc\theta represents in the triangle and calculate its value.

Related theory

Browse the problem library