Find the value of $ an(x) $ for $ x = frac{pi}{4} $

To find the value of $ \tan(x) $ when $ x = \frac{\pi}{4} $, we use the unit circle chart.

For $ x = \frac{\pi}{4} $, the coordinates on the unit circle are (\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}).

The tangent function is defined as:

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

So,

$ \tan\left( \frac{\pi}{4} \right) = \frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} = 1 $

For $ x = frac{pi}{4} $, the coordinates on the unit circle are (frac{sqrt{2}}{2}, frac{sqrt{2}}{2}).

We know that:

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

Therefore,

$ anleft( frac{pi}{4}
ight) = frac{frac{sqrt{2}}{2}}{frac{sqrt{2}}{2}} = 1 $

For $ x = frac{pi}{4} $:

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

So,

$ anleft( frac{pi}{4}
ight) = 1 $

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