The functions (y = x ) and (y = 3x ) differ in their graphical features.

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

Problem

The functions

y = \sin x

and

y = \sin 3x

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

y = \sin 3x

and compare it with the period of

y = \sin x

. (ii) Determine how many zeros

\sin 3x

possesses in the interval

0 \le x \le 2\pi

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

y = \sin 3x

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