ProofWiki:Sandbox/Template

Proof

 * Limit-arc.png

We know that $y=\sin\left(\Theta\right)$ if and only if $\Theta=\arcsin\left(y\right)$, but what is $\Theta$? $\Theta$ is the length of the arc associated with the angle on the circle of radius $1$. One small caveat here. The length of an arc is always a positive number. But if $y$ is negative, we say that the $\arcsin$ is the negative of the length of the arc. This makes the $\arcsin$ and the $\sin$ functions odd, and puts us in line with mathematical convention. Inverse Sine is Odd Function. Without this convention, the derivative of the $\sin$ function would not be continuous. What is the length of this arc? According to Definition:Arc Length, this length is: