Find the sine, cosine, and tangent values for a $45^circ$ angle on the unit circle.

First, we need to convert the angle from degrees to radians. Since $45^\circ$ is in the first quadrant and corresponds to $\frac{\pi}{4}$ radians:

$45^\circ = \frac{\pi}{4} \text{ radians}$

Next, we use the unit circle values for $\frac{\pi}{4}$. The sine and cosine values are:

$\sin\left(\frac{\pi}{4}\right) = \cos\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2}$

The tangent value is the sine value divided by the cosine value:

$\tan\left(\frac{\pi}{4}\right) = \frac{\sin\left(\frac{\pi}{4}\right)}{\cos\left(\frac{\pi}{4}\right)} = 1$

To find the sine, cosine, and tangent of $45^circ$, we first convert it to radians:

$45^circ = frac{pi}{4} ext{ radians}$

We use the unit circle to find the sine and cosine values:

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

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

The tangent is calculated by dividing sine by cosine:

$ anleft(45^circ
ight) = frac{frac{sqrt{2}}{2}}{frac{sqrt{2}}{2}} = 1$

For a $45^circ$ angle:

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

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

$ an(45^circ) = 1$

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