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) What is meant by the reciprocal of a trigonometric ratio? Illustrate your answer by naming any one pair of primary and reciprocal ratios. (ii) Explain, with reasons, why for every acute angle θ\theta the value of csc⁡θ\csc\theta is greater than 11 while the value of sin⁡θ\sin\theta is less than 11. (iii) Describe how knowing the value of a primary trigonometric ratio enables you to determine its reciprocal ratio. Give a brief illustrative example (no numerical calculation is required).

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