Find the tangent of the angle $ heta$ when $ heta$ is $45^circ$ on the unit circle.

To find the tangent of $45^\circ$ on the unit circle, we use the fact that $\tan \theta = \frac{\sin \theta}{\cos \theta}$.

At $45^\circ$, $\sin 45^\circ = \frac{\sqrt{2}}{2}$ and $\cos 45^\circ = \frac{\sqrt{2}}{2}$.

Therefore,

$ \tan 45^\circ = \frac{\sin 45^\circ}{\cos 45^\circ} = \frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} = 1 $

To determine $ an 45^circ$ on the unit circle, recall that $ an heta$ is the ratio of the $y$-coordinate to the $x$-coordinate.

Since $sin 45^circ = frac{sqrt{2}}{2}$ and $cos 45^circ = frac{sqrt{2}}{2}$,

$ an 45^circ = frac{sin 45^circ}{cos 45^circ} = frac{frac{sqrt{2}}{2}}{frac{sqrt{2}}{2}} = 1 $

$ an 45^circ = frac{sin 45^circ}{cos 45^circ} = frac{frac{sqrt{2}}{2}}{frac{sqrt{2}}{2}} = 1 $

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