Draw the graph of for and extend it to using periodicity.

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

Problem

Draw the graph of

y = \tan \theta

for

\theta\in\left(-\dfrac{\pi}{2},\dfrac{\pi}{2}\right)

and extend it to

\theta\in\left(-\dfrac{3\pi}{2},\dfrac{3\pi}{2}\right)

using periodicity. (i) State the domain and range of

y=\tan \theta

as evident from your sketch. (ii) Mark all points in the interval

\left(-\dfrac{3\pi}{2},\dfrac{3\pi}{2}\right)

where the curve meets the

\theta

-axis. (iii) Using the graph, list the intervals within

\left(-\dfrac{3\pi}{2},\dfrac{3\pi}{2}\right)

in which

\tan \theta > 1

and those in which

\tan \theta < -1

. (iv) Verify algebraically that the solution set obtained in part (iii) repeats every

\pi

units along the

\theta

-axis.