Mathematics

Problem

Study of the sine function on one complete revolution. a. (i) Using equal intervals of

\dfrac{\pi}{6}

on the

x

-axis, plot and join the points to obtain a smooth sketch of the graph

y=\sin x

for

0\le x\le2\pi

. b. (ii) With the help of your sketch, determine the set of

x

values in

[0,2\pi]

for which

\sin x\ge\dfrac{1}{2}

. c. (iii) Express your answer from part (ii) in the form of one or more closed intervals.