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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).

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

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