Consider the addition formulae:

Cos(a+b) = cos(a)cos(b) - sin(a)sin(b)

Sin(a+b)=sin(a)cos(b) + sin(b)cos(a)

(I'm going to do the following in degrees, so just remember 90 degrees is π/2 rads, and I'll use x instead of theta, again for ease)

Now let a=90 and b=x.

Then we have

 cos(90-x) =

 cos(90)cos(-x) - sin(90)sin(-x)

Cos(90) = 0 and sin(90) = 1

And cos(-x) = cos(x) [look at the graph of... more