# How to evaluate -arctan(cosx) from ∏/2 to ∏

1. Feb 28, 2012

### mathnoobie

1. The problem statement, all variables and given/known data
The direction is the evaluate the integral, this isn't really a calculus issue, it's more of a trig issue.
∫sinx(dx)/(1+cos^2x) from ∏/2 to ∏

2. Relevant equations
(1/a)arctan(u/a)+c

3. The attempt at a solution
I did all the integrating and ended up at
-arctan(cosx) from ∏/2 to ∏
this is where I'm stuck, I know I'm suppose to use the fundamental theorum of Calculus but I don't know what to do once I plug in ∏/2 and ∏. How do I generate values out of this? Do I draw a triangle? Do I use the unit circle? If so, how would I use it

2. Feb 28, 2012

### Staff: Mentor

This seems pretty straightforward.
-arctan(cos($\pi$)) - (-arctan(cos($\pi$/2)))

What is cos($\pi$)? cos($\pi$/2)?

3. Feb 28, 2012

### mathnoobie

Cos ∏ is -1
Cos ∏/2 is 0 I believe
so then I would take the Arctan(-1)-Arctan(0)
So I would just find on the unit circle where tangent equals -1 and 0, then subtract?

4. Feb 28, 2012

Right.