(a) On the same set of axes, sketch neat labelled graphs of and for . Mark all…

MATHEMATICS · Subjective · AP · AP Precalculus · Trigonometric and Polar Functions · Trigonometric and Polar Functions

Problem

(a) On the same set of axes, sketch neat labelled graphs of

y = \sin x

and

y = \cos x

for

0 \le x \le 2\pi

. Mark all intercepts on the

x

–axis and the

y

–axis. (b) Using your sketch, explain why

\cos x

may be viewed as a horizontal shift of the graph of

\sin x

. State the magnitude and direction of this shift in terms of

\pi

. (c) From the sketch, list: (i) the values of

x

[0,2\pi]

for which

\sin x = 0

, and (ii) the values of

x

[0,2\pi]

for which

\cos x = 0