Find the value of $ an( heta) $ at multiple angles using the unit circle

Let

Using the unit circle, we can find the value of the tangent function for the angles $ heta = frac{pi}{4} $, $ heta = frac{3pi}{4} $, and $ heta = pi $:

1. For $ heta = frac{pi}{4} $:

$ an(frac{pi}{4}) = 1 $

2. For $ heta = frac{3pi}{4} $:

$ an(frac{3pi}{4}) = -1 $

3. For $ heta = pi $:

$ an(pi) = 0 $

Find the values of $ an( heta) $ for the angles $ heta = frac{pi}{6} $, $ heta = frac{pi}{2} $, and $ heta = frac{5pi}{4} $:

1. For $ heta = frac{pi}{6} $:

$ an(frac{pi}{6}) = frac{1}{sqrt{3}} $

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

$ an(frac{pi}{2}) = ext{undefined} $

3. For $ heta = frac{5pi}{4} $:

$ an(frac{5pi}{4}) = 1 $

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