Find the values of $ an(x) $ at different positions on the unit circle

To find the values of $ \tan(x) $ at different positions on the unit circle, we use the definition:

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

First, let

To determine values of $ an(x) $ at various points on the unit circle, use:

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

At $ x = frac{3pi}{4} $:

$ sin(frac{3pi}{4}) = frac{ sqrt{2} }{2}, cos(frac{3pi}{4}) = -frac{ sqrt{2} }{2} $

Therefore,

$ an(frac{3pi}{4}) = frac{ frac{ sqrt{2} }{2} }{ -frac{ sqrt{2} }{2} } = -1 $

At $ x = pi $:

$ sin(pi) = 0, cos(pi) = -1 $

Therefore,

$ an(pi) = frac{0}{-1} = 0 $

To evaluate $ an(x) $ on the unit circle:

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

At $ x = frac{3pi}{2} $:

$ sin(frac{3pi}{2}) = -1, cos(frac{3pi}{2}) = 0 $

Therefore,

$ an(frac{3pi}{2}) = frac{-1}{0} $

which is undefined.

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