Mathematics

Problem

Carry out the following exact evaluations, writing each answer in simplest rationalised radical form. a. (a) For

\theta = 30^{\circ}

, find

\tan\theta,\;\sec\theta

and

\csc\theta

. b. (b) For

\theta = \dfrac{\pi}{4}

, write the coordinate pair

(\cos\theta,\sin\theta)

and hence evaluate the expression

E = 2\sin\theta + \sqrt{3}\,\cos\theta

. c. (c) For

\theta = 60^{\circ}

, compute

\cot\theta + \tan\theta

and simplify the result.