Find the values of $ an( heta)$, $sin( heta)$, and $cos( heta)$ for $ heta = 45^circ$

To find the values of $\tan(\theta)$, $\sin(\theta)$, and $\cos(\theta)$ for $\theta = 45^\circ$:

First, we note that $\theta = 45^\circ$ is in the first quadrant of the unit circle.

The coordinates of the point on the unit circle at $\theta = 45^\circ$ are:

$\left( \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right)$

Therefore:

$\sin(45^\circ) = \frac{\sqrt{2}}{2}$

$\cos(45^\circ) = \frac{\sqrt{2}}{2}$

Using the definition of tangent:

$\tan(45^\circ) = \frac{\sin(45^\circ)}{\cos(45^\circ)} = 1$

To find the values of $ an( heta)$, $sin( heta)$, and $cos( heta)$ for $ heta = 45^circ$:

We know that at $ heta = 45^circ$ on the unit circle:

$sin(45^circ) = frac{sqrt{2}}{2}$

$cos(45^circ) = frac{sqrt{2}}{2}$

Therefore:

$ an(45^circ) = 1$

At $ heta = 45^circ$:

$sin(45^circ) = frac{sqrt{2}}{2}$

$cos(45^circ) = frac{sqrt{2}}{2}$

$ an(45^circ) = 1$

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