Definition:Sine/Definition from Circle/Second Quadrant

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Consider a unit circle $C$ whose center is at the origin of a cartesian plane.


Let $P = \tuple {x, y}$ be the point on $C$ in the second quadrant such that $\theta$ is the angle made by $OP$ with the $x$-axis.

Let $AP$ be the perpendicular from $P$ to the $x$-axis.

Then the sine of $\theta$ is defined as the length of $AP$.

Hence in the second quadrant, the sine is positive.