Question

What is the period of f(x)= (sinx)(cosx)?

Answer 1

hmm, can we do calculus?

Answer 2

Yeah

Answer 3

Seems complicated, just use a trig identity

Answer 4

we know when the zeros are; sin(0)=sin(180)=cos(90)=cos(270) = 0

Answer 5

i want to say pi, but havent determined a good approach

Answer 6

f' = sin(-sin) + cos(cos)
= cos^2 - sin^2
= cos(2x)
which has a period of pi

Answer 7

but that just means that at every multiple of pi we have a min or a max

Answer 8

f'' = -2sin(2x) would tell us of concavity

Answer 9

Yeah

Answer 10

might have my f' interpreted a bit off :) whenever cos(2x)=0 we have a min/max

Answer 11

2x = (2n+1)*pi/2

x = (2n+1)*pi/4

so min/max are at: pi/4, 3pi/4, 5pi/4, 7pi/4 ...

http://www.wolframalpha.com/input/?i=y%3Dsin%28x%29cos%28x%29

yeah, its pi lol

Answer 12

Thanks Very Much !

Answer 13

youre welcome, wish i knew of a simpler process, but they all tend to elude me :) teh derivetives should give some proof to it if you can sort thru it.