What is the value of $ an(45°)$ on the unit circle?

To find the value of $\tan(45°)$ on the unit circle, we use the definition of tangent:

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

At $\theta = 45°$, we have:

$\sin(45°) = \frac{\sqrt{2}}{2}$

$\cos(45°) = \frac{\sqrt{2}}{2}$

Thus,

$\tan(45°) = \frac{\sin(45°)}{\cos(45°)} = \frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} = 1$

So, the value of $\tan(45°)$ is $1$.

To determine $ an(45°)$, we refer to the unit circle properties:

$ an(45°) = frac{sin(45°)}{cos(45°)}$

Given that

$sin(45°) = frac{sqrt{2}}{2}$

$cos(45°) = frac{sqrt{2}}{2}$

It follows:

$ an(45°) = frac{frac{sqrt{2}}{2}}{frac{sqrt{2}}{2}} = 1$

Therefore, $ an(45°)$ equals $1$.

Using the unit circle, we know:

$ an(45°) = frac{sin(45°)}{cos(45°)}$

With

$sin(45°) = frac{sqrt{2}}{2}$

$cos(45°) = frac{sqrt{2}}{2}$

So,

$ an(45°) = 1$

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