The Unit Circle

It turns out that a nice value to take for the hypotenuse is $h=1$. When this happens, we get points in the $xy$-plane on the unit circle. Notice that sine and cosine become $$ \cos(\theta) = \frac{x}{h} = x\quad\quad \sin(\theta) = \frac{y}{h} = y $$ which means $\cos(\theta)$ is the $x$-coordinate of the point on the unit circle at angle $\theta$, and $\sin(\theta)$ is the $y$-coordinate of the point on the unit circle at angle $\theta$, where $\theta$ represents the angle measured from the positive $x$-axis in the counter-clockwise direction. All of our trigonometric ratios can be thought of as real-valued trigonometric functions of $\theta$.

You should memorize the values of $\sin(\theta)$ and $\cos(\theta)$ at the important angles in the first quadrant of the unit circle:

The video examples below will show you how to use the CAST Rule to evaluate trigonometric functions at important angles in the other quadrants.