Question

I have
F(theta)=[cos(pi.cos(theta)+n*pi/4)+(-1)^n.cos(3pi.cos(theta)+n*pi/4)]²

How do i find theta as function of n pi/4 to maximize F(theta)?

Answer 1

n can assume values 0,1,2,3

Answer 2

If n is even, we can try simplifying F using the identity:
cos(A) + cos(B) = 2cos((A+B)/2)cos((A-B)/2)

For odd n it will be the sine function with a -2 in the front.

Answer 3

i was trying to derivate it

Answer 4

Yes, \(\Large \frac{dF}{d\theta} = 0\).
But I was wondering if this has to be solved separately for even n and odd n and perhaps the solution, if possible, combined in the end.

Answer 5

Can you solve for n odd??

Answer 6

is this the function?
\[F(\theta)=\left[\cos\left(\pi\cos\theta+\frac{n\pi}{4}\right)+(-1)^n\cos\left(3\pi\cos\theta+\frac{n\pi}{4}\right)\right]^2\]

Answer 7

@Orion1213 , yes