The (extended) unit circle

A solid understanding of the unit circle makes trigonometry much easier to understand. You should absolutely understand that the East, North, West, and South points (shown in green below) have angle measures that are multiples of \(\pi/2\) and their coordinates are $$(1,0), \; (0,1) \; (-1,0) \; \text{ and } \; (0,-1).$$ This makes it very easy to read off the values of the sine and cosine. The trig values of \(\pi/6\) and \(\pi/3\) can be derived from an equilateral triangle and the trig values of \(\pi/4\) can be derived from an isosceles right triangle. Again, an understanding of the unit circle helps you quickly see the trig values of related angles, like \(-7\pi/6\).

You can use the interactive version of the unit circle to check values of the standard angles between zero and \(2\pi\). You can also hit the "Show more angles" button, if you're curious about some crazier angles.