what is the maximum value of sinthetacostheta?

Answer 1

let y = sinØ cosØ
dy/dØ = sinØ(-sinØ) + cosØ(cosØ)
= cos^2 Ø - sin^2 Ø
= cos 2Ø

but for a max/min, dy/dØ = 0
cos 2Ø = 0
2Ø = π/2 or 3π/2 , (90° or 270°)
Ø = π/4 or 3π/4 , (45° or 135°)

when Ø = π/4
sin(π/4) (cos(π/4) = (1/√2)(1/√2) = 1/2
for Ø = 3π/2 we get -1/2

so the max is 1/2

Answer 2

seems like a lot of work

y = 1/2 sin(2θ)

max value is thus 1/2

Answer 3

Yup, you got me!
one big DUH!