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ex: sin(PI/6) = "1/2"

My problem stems from obtaining the ratios from points on the unit circle, x**2 + y**2 = 1

I need to be able to calculate the point P(x,y) from the angle (a) on the unit circle without using any trigonometric functions because I will use those points to define the functions.

Some of the people I have asked suggested using calculus to find the coordinates. However, I don't know much about calculus or advanced trig.

Would Pythagorean's theory help in any way? Would it be more beneficial to use Calculus?

Anything to point me in the right direction would help greatly.