The graph of a trigonometric function satisfies the following properties: • Amplitude

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

Problem

The graph of a trigonometric function

f

satisfies the following properties: • Amplitude

=2

. • Period

=\pi

. • The graph passes through the origin

\bigl(0,0\bigr)

and is increasing there. (a) Write an explicit algebraic expression for

f(x)

in its simplest form. (b) Sketch the graph of

f(x)

for two complete periods, i.e. for

0\le x\le 2\pi

. (c) Using the graph or otherwise, state the range of

f