Find the values of $ an( heta) $ for specific angles on the unit circle

To find the values of $ \tan(\theta) $ for specific angles on the unit circle, consider the angles $ \theta = \frac{\pi}{4}, \frac{3\pi}{4}, \frac{5\pi}{4}, \frac{7\pi}{4} $:

For $ \theta = \frac{\pi}{4} $:

$ \tan\left(\frac{\pi}{4}\right) = 1 $

For $ \theta = \frac{3\pi}{4} $:

$ \tan\left(\frac{3\pi}{4}\right) = -1 $

For $ \theta = \frac{5\pi}{4} $:

$ \tan\left(\frac{5\pi}{4}\right) = 1 $

For $ \theta = \frac{7\pi}{4} $:

$ \tan\left(\frac{7\pi}{4}\right) = -1 $

Let

Find the values of $ an( heta) $ for $ heta = 0, pi, frac{pi}{2}, frac{3pi}{2} $:

For $ heta = 0 $:

$ an(0) = 0 $

For $ heta = pi $:

$ an(pi) = 0 $

For $ heta = frac{pi}{2} $:

$ anleft(frac{pi}{2}
ight) $ is undefined

For $ heta = frac{3pi}{2} $:

$ anleft(frac{3pi}{2}
ight) $ is undefined

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