Determine $ an( heta) $ from the unit circle at point $ P(x,y) $

To determine $ \tan(\theta) $ from the unit circle at point $ P(x,y) $, recall that

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

On the unit circle, you have $ P(x,y) = (\cos(\theta), \sin(\theta)) $, so

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

Ensure that $ x \neq 0 $ to avoid division by zero.

To find the tangent of an angle $ heta $ using the unit circle coordinates $ (x,y) $, use the definition of tangent:

$ an( heta) = frac{sin( heta)}{cos( heta)} $

Given that $ P(x,y) $ is a point on the unit circle, where $ x = cos( heta) $ and $ y = sin( heta) $,

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

This equation holds as long as $ x
eq 0 $.

To calculate $ an( heta) $ from the unit circle coordinates, use

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

where $ (x,y) $ are the coordinates of the point on the unit circle, assuming $ x
eq 0 $.

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