Mathematics

Problem

The curves

y=\sin x

and

y=\sin 3x

are drawn on the same set of axes. a. (i) Show algebraically that

\sin 3x=\sin x

whenever

x=n\pi

, where

n\in\mathbb{Z}

. b. (ii) Explain why the points whose

x

-coordinates are integral multiples of

\pi

are points of intersection of the two curves. c. (iii) State two other distinct

x

-values in the interval

0<x<2\pi

at which the curves intersect, giving reasons for your answer.