$ ext{Find the sine, cosine, and tangent values for an angle of } 45^circ ext{ on the unit circle.}$

$\text{For an angle of } 45^\circ \text{ on the unit circle:}$

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

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

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

$ ext{To find the trigonometric values for } 45^circ ext{ on the unit circle, we use the following:}$

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

$ ext{Rationalizing the denominator:}$

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

$ an(45^circ) = 1$

$ ext{Using the unit circle for } 45^circ:$

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

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