Given a point $P$ on the unit circle with coordinates $(x, y)$, find the value of $cot( heta)$ where $ heta$ is the angle formed by the positive $x$-axis and the line segment $OP$.

Given a point $P(x, y)$ on the unit circle:

$x = \cos(\theta), \quad y = \sin(\theta)$

The cotangent of angle $\theta$ is:

$\cot(\theta) = \frac{\cos(\theta)}{\sin(\theta)}$

Since $x = \cos(\theta)$ and $y = \sin(\theta)$, we can write:

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

Therefore, the value of $\cot(\theta)$ is:

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

Given the point $P(x, y)$ on the unit circle:

$x = cos( heta), quad y = sin( heta)$

We know that cotangent is the reciprocal of tangent. Thus,

$cot( heta) = frac{1}{ an( heta)}$

Since $ an( heta) = frac{sin( heta)}{cos( heta)}$, we have:

$cot( heta) = frac{1}{frac{sin( heta)}{cos( heta)}} = frac{cos( heta)}{sin( heta)}$

By substituting $x$ and $y$:

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

Given $P(x, y)$ on the unit circle:

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

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