Consider the function restricted to the interval .

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

Problem

Consider the function

g(x)=\tan x

restricted to the interval

-\tfrac{3\pi}{2}<x<\tfrac{3\pi}{2}

. (i) Find the equations of all vertical asymptotes of the graph of

g

in the given interval. (ii) List all zeros of

g

in the same interval. (iii) Construct a table of signs of

g(x)

for each sub-interval separated by the vertical asymptotes and zeros. (iv) Hence sketch the graph of

y=\tan x

on the interval

-\tfrac{3\pi}{2}<x<\tfrac{3\pi}{2}

, showing the asymptotes and the behaviour of the curve as it approaches them.