Sine (source code)
= Sine
{title2=$\sin$}
{wiki}
For a real <angle> $\theta$, $\sin\theta$ is the vertical coordinate on the <unit circle> reached by a counterclockwise <rotation> through $\theta$ <radians>. For an acute <angle> in a <right triangle>, it is the opposite side divided by the <hypotenuse>. In particular,
$$
\sin0=0,\qquad \sin(\pi/6)=\frac12,\qquad
\sin(\pi/2)=1,\qquad \sin\pi=0.
$$
The first-quarter rise and second-quarter fall are visible in the circle projection; the lower semicircle gives negative values.
Reflecting the <unit circle> across the horizontal axis gives $\sin(-\theta)=-\sin\theta$, so <sine> is an <odd function>. A full turn gives $\sin(\theta+2\pi)=\sin\theta$, making it a <periodic function>. For real arguments, its range is $[-1,1]$ and its <zeros of a function> occur at $\theta=k\pi$ for <integers> $k$. The <cosine> describes the perpendicular coordinate of the same point, and the <Pythagorean trigonometric identity> keeps their two values tied together.
Back to article page
