Find the value of $ an$ for the angle $45^{circ}$ on the unit circle.

To find the value of $\tan 45^{\circ}$ on the unit circle, we use the definition of $\tan$:

$\tan \theta = \frac{\sin \theta}{\cos \theta}$

For $\theta = 45^{\circ}$, we know that $\sin 45^{\circ} = \frac{\sqrt{2}}{2}$ and $\cos 45^{\circ} = \frac{\sqrt{2}}{2}$.

Substituting these values in, we get:

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

So, the value of $\tan 45^{\circ}$ is 1.

Let’s determine the value of $ an$ at $45^{circ}$ using the unit circle properties:

The coordinates of the point on the unit circle at $45^{circ}$ are $(cos 45^{circ}, sin 45^{circ}) = left(frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$.

We know $ an heta$ is defined as:

$ an heta = frac{sin heta}{cos heta}$

Substituting the values:

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

Thus, the value of $ an 45^{circ}$ is indeed 1.

Using the unit circle:

$ an 45^{circ} = frac{sin 45^{circ}}{cos 45^{circ}}$

Since $sin 45^{circ} = cos 45^{circ} = frac{sqrt{2}}{2}$, we have:

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

Start Using PopAi Today