You have seen that you can calculate values of the sine function using right triangles formed by a radius of the unit circle. Values of $θ$ that result in $30^\circ-60^\circ-90^\circ$ or $45^\circ-45^\circ-90^\circ$ triangles are frequently used because their sine and cosine values can be expressed exactly, without using a calculator. You should learn to recognize these values when you see them. The same is true for values of $\text{cos}\left(θ\right)$ and $\text{sin}\left(θ\right)$ that correspond to the $x$- and $y$-intercepts of the unit circle.

The central angles that correspond to these “special” values of $θ$ are $0^\circ, 30^\circ, 45^\circ, 60^\circ, 90^\circ, 120^\circ, 135^\circ, 150^\circ, 180^\circ, 210^\circ, 225^\circ, 240^\circ, 270^\circ, 300^\circ, 315^\circ, \text{and }330^\circ$. What these angles have in common is that they are all multiples of $30^\circ$ or $45^\circ$.

Copy and complete a table like the one below for all special angles between $0^\circ$ and $360^\circ$.