# Rolls Theorem (trig functions)

1. Feb 23, 2015

### Jonathan_Kyle

1. The problem statement, all variables and given/known data
f(x) = sin5x ; [π/5,2π/5] finding the point c which f'(x) =0. I understand the theorem and how to complete it, my issue is using the triq functions

2. Relevant equations
f'(x) = 5cos5x

3. The attempt at a solution
5cos5x=0
cos5x=0
5x=π/3
x=π/15
my answer is not correct, I am using mathlab and I cannot see how they came to their answer

2. Feb 23, 2015

cos5x=0
5x=π/2 or 3π/2
x=π/10 or 3π/10
x=π/10 is not in domain so answer is 3π/10

3. Feb 23, 2015

### Jonathan_Kyle

Thank you for the reply, I am obviously doing something wrong between;
cos5x=0
and
5x= π/2 or 3π/2 ( i understand where you get 3π/2, just another revolution from π/2)
what i don't understand is how you got π/2, I was under the impression that you take the inverse of cosine from each side of the equation to isolate x on the left hand side. Furthermore, I was told that finding the inverse of the cosine function is π/3, because that gives you 1/2. I think I was just given some back information on how to solve that portion of the problem.

4. Feb 23, 2015

### SteamKing

Staff Emeritus
Not quite. Remember, 1 revolution = 2π radians, so it's a half revolution.

If you were trying to find θ such that cos θ = 0, what would be the value of θ in this case? For what angles is the cosine zero?

You can use the unit circle to figure this out, and you should have memorized where sin θ = 0, cos θ = 0, tan θ = 1, etc.