(Comprehensive analysis of on a given domain)

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

Problem

(Comprehensive analysis of

\tan x

on a given domain) (i) State the domain of

y=\tan x

in the open interval

(-2\pi,2\pi)

. (ii) List all zeros of

y=\tan x

that lie in

(-2\pi,2\pi)

. (iii) Write the equations of all vertical asymptotes of

y=\tan x

in this interval. (iv) Sketch the graph of

y=\tan x

for

x\in(-2\pi,2\pi)

, clearly showing the zeros and asymptotes obtained above. (v) Give a brief justification for why the parent function

y=\tan x

has no maximum or minimum points.