Working Out Trig Ratios for Angles with Large Fractions in the Unit Circle

[alpha01]

Just trying to find a way to work out the trig ratios for angles with large fracetions in the unit circle (e.g. sin(15pi/2) etc..)

for angles with smaller fractions like cos(-7pi/4) i can solve easily like this: 7/4 = 1.75 = 45 degree (pi/4) angle in the 1st quadrant (because its negative), therefore cos of this angle = 1/sqrt(2)

i understand for larger fractions i need to first put them in the form of n.2pi + theta (where n.2pi is the number of full revolutions and theta is the angle remaining at the end)

how can i put angles like sin(15pi/2) into the form n.2pi + theta?

thanks

 

[sutupidmath]

$$sin\frac{15\pi}{2}=sin(7\pi+\frac{\pi}{2})=sin(8\pi-\frac{\pi}{2})$$