Mathematics

Problem

The functions

y = \sin x

and

y = \sin 3x

differ in their graphical features. a. (i) State the period of

y = \sin 3x

and compare it with the period of

y = \sin x

. b. (ii) Determine how many zeros

\sin 3x

possesses in the interval

0 \le x \le 2\pi

and explain your reasoning. c. (iii) Sketch one complete cycle of

y = \sin 3x

, clearly labelling the intercepts on the axes and the maximum and minimum values.