Consider the function

MATHEMATICS · Subjective · CBSE · Mathematics · Trigonometric Functions · Trigonometric Functions

Problem

Consider the function y=tan⁡xy = \tan x. (a) State the fundamental period of tan⁡x\tan x. (b) Sketch the graph of y=tan⁡xy = \tan x for the interval −3π2<x<3π2-\tfrac{3\pi}{2} < x < \tfrac{3\pi}{2}. Indicate clearly all intercepts on the xx–axis and the positions of the vertical asymptotes. (c) Write the equations of all vertical asymptotes that lie inside the given interval. (d) From your sketch, determine the intervals inside −3π2<x<3π2-\tfrac{3\pi}{2} < x < \tfrac{3\pi}{2} on which tan⁡x\tan x is negative.

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