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

[mathnoobie]

Homework Statement

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 ∏

Homework Equations

(1/a)arctan(u/a)+c

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

 

[Mark44]

Homework Statement

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 ∏

Homework Equations

(1/a)arctan(u/a)+c

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

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

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

 

[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?

 

[Mark44]

Right.