Properties of the tangent curve over several periods.

MATHEMATICS · Multi-part · CBSE · Mathematics · Trigonometric Functions · Trigonometric Functions

Problem

Properties of the tangent curve over several periods. (i) Draw a well-labelled sketch of

y=\tan x

for

x\in[-3\pi,3\pi]

, showing at least three successive asymptotes and indicating their equations. (ii) Mark on your sketch the points corresponding to

x=0,\;\pm\dfrac{\pi}{4},\;\pm\dfrac{3\pi}{4}

and label the function values. (iii) Using the graph, write the intervals in

[-3\pi,3\pi]

for which

\tan x>1