Find the value of $ an( heta)$ on the unit circle where $ heta$ is $frac{pi}{4}$.

On the unit circle, the coordinates for $\theta = \frac{\pi}{4}$ are $\left( \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right)$.

Therefore, $\tan(\frac{\pi}{4})$ is calculated as:

$\tan(\frac{\pi}{4}) = \frac{\sin(\frac{\pi}{4})}{\cos(\frac{\pi}{4})} = \frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} = 1$

The angle $frac{pi}{4}$ on the unit circle corresponds to the coordinates $left( frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$.

We find $ an(frac{pi}{4})$ as follows:

$ an(frac{pi}{4}) = frac{y}{x} = frac{frac{sqrt{2}}{2}}{frac{sqrt{2}}{2}} = 1$

At $ heta = frac{pi}{4}$, the coordinates on the unit circle are $left( frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$.

So, $ an(frac{pi}{4}) = 1$.

Start Using PopAi Today