Mathematics

Problem

Answer the following questions concerning the trigonometric equation

\tan\theta = \tan\alpha

, where

\alpha

is a fixed angle. a. (i) Explain why the function

\tan\theta

repeats its values after an increase of

\pi

radians, whereas

\sin\theta

and

\cos\theta

repeat after

2\pi

radians. b. (ii) Using the property stated in part (i), obtain the general solution of the equation

\tan\theta = \tan\alpha

. c. (iii) How many distinct solutions does the equation

\tan\theta = \tan 60^{\circ}

have in any interval of length

\pi

? Justify your answer.