Answer the following questions about the tangent function.

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

Problem

Answer the following questions about the tangent function. (i) State the identities that relate

\tan\theta

and

\cot\theta

\sin\theta

and

\cos\theta

. (ii) Give a clear reason why

\tan\theta

is not defined for

\theta = \dfrac{\pi}{2}+k\pi

, where

k\in\mathbb Z

. (iii) Using quadrant–sign rules, decide whether

\tan120^\circ

and

\tan210^\circ

are positive or negative. Justify each answer.