Answer the following questions related to reciprocal trigonometric functions.

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

Problem

Answer the following questions related to reciprocal trigonometric functions. (i) Define sec⁡θ,  csc⁡θ\sec\theta,\;\csc\theta and cot⁡θ\cot\theta in terms of sin⁡θ\sin\theta and cos⁡θ\cos\theta. (ii) Rewrite the expression sec⁡θ−csc⁡θcot⁡θ\displaystyle \frac{\sec\theta-\csc\theta}{\cot\theta} solely in terms of sin⁡θ\sin\theta and cos⁡θ\cos\theta and simplify it as far as possible. (iii) Explain briefly why the simplified form obtained in part (ii) is more convenient than the original form when one needs to evaluate the expression at a specific numerical value of θ\theta, say θ=45∘\theta=45^{\circ}."

Related theory

Browse the problem library