Calculate the value of $ an( heta) $ at $ heta = 45° $ using the unit circle

To calculate $ \tan(\theta) $ at $ \theta = 45° $ using the unit circle, we note that at $ 45° $, the coordinates on the unit circle are $ \left( \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right) $.

The formula for $ \tan(\theta) $ is:

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

Since at $ \theta = 45° $:

$ \sin(45°) = \frac{\sqrt{2}}{2} $

$ \cos(45°) = \frac{\sqrt{2}}{2} $

The value of $ \tan(45°) $ is:

$ \tan(45°) = \frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} = 1 $

To find $ an( heta) $ at $ heta = 45° $ using the unit circle, remember that the coordinates at $ 45° $ are $ left( frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight) $.

Using the formula:

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

We get:

$ an(45°) = frac{frac{sqrt{2}}{2}}{frac{sqrt{2}}{2}} = 1 $

To find $ an( heta) $ at $ heta = 45° $ using the unit circle:

$ an(45°) = frac{sin(45°)}{cos(45°)} = frac{frac{sqrt{2}}{2}}{frac{sqrt{2}}{2}} = 1 $

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