How do I verify that $\sin (\theta)$ and $\cos (\theta)$ are functions? I am studying pre-calculus mathematics at the moment, and I need help in verifying if  $\sin (\theta)$ and $\cos (\theta)$ are functions? I want to demonstrate that for any angle $\theta$ that there is only one associated value of $\sin (\theta)$ and $\cos (\theta)$. How do I go about showing this?

It follows from the definition of $\sin(\theta)$ as a ratio of length of $\theta$'s opposite side to hypotenuse (Wikipedia).
As long as hypotenuse length is not equal to zero (otherwise the triangle degenerates into line or point), the division is a function which yields only one associated value.
