How is the $\cos A$ and $\sin A$ equal to coordinates on the unit circle? I have seen them becoming coordinates in first quadrant but I want to know how are they equal to coordinates in 2nd quadrant.
2026-04-01 17:22:24.1775064144
Trigonometry unit circles
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1
Note that by definition $\cos A$ and $\sin A$ are precisely the coordinates of the point P(x,y) on the unitary circle such that ray OP forms an angle A with positive x axis (usually assuming as positive the counterclockwise direction).
Since the equation for the unit circle is
$$x^2+y^2=1 \iff \cos^2 A+\sin^2 A=1$$
which is the foundamental trigonometric identity, valid of course for every A and quadrant, from which all others trigonometric identities derive.