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

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To calculate trigonometric ratios for angles with large fractions in the unit circle, first convert the angle into the form n.2π + θ, where n represents the number of full revolutions and θ is the remaining angle. For example, sin(15π/2) can be simplified to sin(7π + π/2) or sin(8π - π/2). This method allows for easier evaluation of the sine and cosine functions by identifying the equivalent angle within the first revolution. Understanding this conversion process is essential for accurately determining trig ratios for complex angles.
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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
 
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sin\frac{15\pi}{2}=sin(7\pi+\frac{\pi}{2})=sin(8\pi-\frac{\pi}{2})
 

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