Mathematics

Problem

Examine the behaviour of the tangent function. a. (i) Sketch the graph of

y=\tan x

for the interval

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

. Indicate all vertical asymptotes and zeros. b. (ii) Using the graph, solve the inequality

\tan x > 1

within the same interval. c. (iii) Extend your result to write the complete set of real solutions of the inequality

\tan x > 1

. Justify your answer with reference to the periodicity of the tangent function.