Rewrite with only sin(x) and cos(x). sin(3x)

sin 3x = sin (2x + x)

= sin2x cos x + cos 2x sin x   (using the compound angle identity)

= 2sin x cos x.cos x  (1 - 2sin^2x) sinx     (using identities for sin2x and cos2x)

=  2 sin cos^2 x + sin x - 2 sin^3 x

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."