Find the values of $sin 45^circ$ and $cos 45^circ$ in the unit circle.

First, recall that in the unit circle, an angle of 45 degrees corresponds to $\frac{\pi}{4}$ radians.

From trigonometric identities:

$\sin \frac{\pi}{4} = \frac{\sqrt{2}}{2}$

$\cos \frac{\pi}{4} = \frac{\sqrt{2}}{2}$

Therefore, the values are:

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

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

To find the sine and cosine values for a 45-degree angle in the unit circle, we convert degrees to radians: $45^circ = frac{pi}{4}$ radians.

Using the unit circle properties:

$sin frac{pi}{4} = frac{1}{sqrt{2}} = frac{sqrt{2}}{2}$

$cos frac{pi}{4} = frac{1}{sqrt{2}} = frac{sqrt{2}}{2}$

So, the sine and cosine of 45 degrees are:

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

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

In the unit circle, the sine and cosine for 45 degrees (or $frac{pi}{4}$ radians) are both $frac{sqrt{2}}{2}$:

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

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

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