Mathematics

Problem

Consider the function

f(x)=\sin x\,\cos x

. a. (a) Prove that

f(x)

is an odd function. b. (b) Determine all zeros of

f(x)

in the interval

[-2\pi,2\pi]

. c. (c) Sketch the graph of

y=f(x)

for

x\in[-2\pi,2\pi]

, clearly indicating intercepts and turning points. d. (d) Using your graph or otherwise, state the maximum and minimum values of

f(x)

and the corresponding values of

x

at which they occur in

[-2\pi,2\pi]