Simplify

\(\cos\left(\dfrac{3\pi}{2}-\Theta\right)\\=-\sin \Theta\)

cos(3pi/2) = 0, sin(3pi/2) = -1,  0cos(theta) + -1sin(theta) = -sin(theta)

cos((3π/2) - ϴ)

\(cos((3π/2) - \theta)\\ =\text{change to degrees}\\ =cos(270-\theta)\\ =cos(180+(90-\theta))\\ =-cos(90-\theta)\\ =-sin(\theta)\)

I think Max is right in that not all this working is really needed.  

But it is easier for me to think through this way :)