Can someone help me maximize a function?

[PowerMacG5]

I am trying to maximize the function on the interval -Pi/2..Pi/2

y = 1-4x^2/Pi^2 - cos(x)

When I get the derivative, I get:

dy/dx = -8x/Pi^2 + sin(x)

I have no idea how to solve that when dy/dx = 0. Can someone help me by putting me on the right track? Thanks in advance.

 

[Triumph]

well the answer is zero, cause i graphed the derivative.... your derivative is right at least.

 

[PowerMacG5]

Originally posted by: Triumph
well the answer is zero, cause i graphed the derivative.... your derivative is right at least.

Zero is a minimum. There are two maximum, around 1.1, and -1.1 (those are not exact, just what I get when I look at the graph). In Mathematica, I get a numerical approximation as +/-1.09882 when I use the Maximize function, but I need exact values.