To complete the equivalence statement:
- The degree value that corresponds to \( \frac{\pi}{4} \) radians is \( 45^\circ \).
- The exact value of \( \sin\left(\frac{\pi}{4}\right) \) is \( \frac{\sqrt{2}}{2} \).
So the completed statement is: \[ \sin 45^\circ = \sin\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2} \]