Find the sine, cosine, and tangent of an angle on the unit circle at $45^circ$.

To find the sine, cosine, and tangent of a $45^\circ$ angle, we start by remembering that on the unit circle:

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

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

$\tan(45^\circ) = 1$

Therefore, the sine, cosine, and tangent of $45^\circ$ are $\frac{\sqrt{2}}{2}$, $\frac{\sqrt{2}}{2}$, and $1$ respectively.

On the unit circle, the coordinates of the point corresponding to $45^circ$ are:

$left( cos(45^circ), sin(45^circ)
ight) = left( frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$

Since the tangent function is the ratio of the sine to the cosine:

$ an(45^circ) = frac{sin(45^circ)}{cos(45^circ)} = frac{frac{sqrt{2}}{2}}{frac{sqrt{2}}{2}} = 1$

Thus, the sine, cosine, and tangent of $45^circ$ are $frac{sqrt{2}}{2}$, $frac{sqrt{2}}{2}$, and $1$ respectively.

For $45^circ$:

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

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

$ an(45^circ) = 1$

Therefore, the values are $frac{sqrt{2}}{2}$, $frac{sqrt{2}}{2}$, and $1$ respectively.

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