## Precalculus (6th Edition) Blitzer

The $\tan t$ is defined as $\frac{y}{x}$ where $\left( x,y \right)$ is the point on the unit circle that corresponds to $t$.
If $t$ is a real number and $P=\left( x,y \right)$ is a point on a unit circle that corresponds to $t,$ then the value of $\tan t$ is: $\tan t=\frac{y}{x}$ For example: If there is a point on unit circle that is $\left( \frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2} \right)$ that corresponds to the real number $t$, where the x-coordinate is $\frac{\sqrt{2}}{2}$ and the y-coordinate is $\frac{\sqrt{2}}{2}$, then the tan of $t$ is: \begin{align} & \tan t=\frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} \\ & \tan t=1 \end{align} Thus, $\tan t$ is defined as $\frac{y}{x}$ where $\left( x,y \right)$ is the point on the unit circle that corresponds to $t$.