(Zeros and extrema of on a specified interval)

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

Problem

(Zeros and extrema of

\sin x

on a specified interval) (i) List all the values of

x

in the interval

[-4\pi, 3\pi]

for which

\sin x=0

. (ii) Determine the coordinates of every maximum and minimum point of the graph

y=\sin x

that lies inside the same interval. (iii) How many distinct points of the graph

y=\sin x

lie on the

x

-axis between

x=-4\pi

and

x=3\pi

, inclusive? Justify your answer.