Find the value of $ an( heta)$ given a point on the unit circle

Given a point on the unit circle at coordinates $(x, y)$, find the value of $\tan(\theta)$ where $\theta$ is the angle formed by the radius connecting the point to the origin.

Using the definition of tangent in the unit circle:

$\tan(\theta) = \frac{y}{x}$

For example, if the point on the unit circle is $(\frac{1}{2}, \frac{\sqrt{3}}{2})$, then:

$\tan(\theta) = \frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}} = \sqrt{3}$

Given a point on the unit circle with coordinates $(x, y)$, the value of $ an( heta)$ can be calculated as follows:

Recall that $ an( heta)$ is the ratio of the y-coordinate to the x-coordinate.

$ an( heta) = frac{y}{x}$

Consider the point $(-frac{sqrt{2}}{2}, frac{sqrt{2}}{2})$ on the unit circle. The tangent of the angle $ heta$ is:

$ an( heta) = frac{frac{sqrt{2}}{2}}{-frac{sqrt{2}}{2}} = -1$

On the unit circle, the tangent of an angle $ heta$ can be found using the coordinates $(x, y)$ of the point where the terminal side of the angle intersects the circle. The formula is:

$ an( heta) = frac{y}{x}$

If the point is $(0, 1)$:

$ an( heta) = frac{1}{0}$ is undefined

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