Unit Circle

The Unit Circle is a circle of radius 1. It is useful as certain angles have memorable coordinates that are helpful for solving trig problems by hand.

Using the Unit Circle for sin, cos, tan

$\sin \theta$ is equal to the y value of the coordinate
$\cos \theta$ is equal to the x value
$\tan \theta$ is equal to the y value divided by the x value¹⁾.

Note that for $\tan \theta$, 90° and 270° ($\frac{\pi}{2}$ and $\frac{3\pi}{2}$ rad) are undefined as you cannot divide by zero²⁾. When calculating inverse trig functions, the solution is restricted between I and IV for $\sin$ and $\tan$, and I and II for $\cos$.

¹⁾

this uses the identity $\tan \theta = \frac{\sin \theta}{\cos \theta}$

²⁾

x values, or $\cos \theta$ is equal to zero in these two situations