Chapter 3 - Radian Measure and the Unit Circle - Section 3.3 The Unit Circle and Circular Functions - 3.3 Exercises - Page 123: 3

$\frac{\sqrt 2}{2}$

$\sin \frac{\pi}{4}$ is the y-coordinate of the point on the unit circle through which the terminal side of angle $\frac{\pi}{4}$ passes. From the solution of excercise 1, we see that $y=\frac{\sqrt 2}{2}$.