Answer the questions below with reference to the graph of .

MATHEMATICS · Multi-part · AP · AP Precalculus · Trigonometric and Polar Functions · Trigonometric and Polar Functions

Problem

Answer the questions below with reference to the graph of

y=\cos x

. (a) Sketch the graph of

y=\cos x

for

-\pi\le x\le2\pi

. Mark on your diagram: • all

x

–intercepts with exact coordinates, • all maximum and minimum points with exact coordinates. (b) Using your sketch, state the set of all

x

in the interval

-\pi\le x\le2\pi

for which

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

. Give your answer in interval notation. (c) From the graph, write down the period of the cosine function and comment on whether

\cos x

is an even or an odd function, justifying your answer from the symmetry of the curve.