Chapter 7 - Trigonometric Identities and Equations - 7.4 Double-Angle and Half-Angle Identities - 7.4 Exercises - Page 694: 63

$\displaystyle \frac{\sqrt{5}}{5}$

Letting $A=2\theta, $ we express $\displaystyle \theta=\frac{A}{2},$ whose sine is positive as it terminates in Q.I. Half-Angle identity: $\displaystyle \sin\frac{A}{2}=+\sqrt{\frac{1-\cos A}{2}}=\sqrt{\frac{1-0.6}{2}}$ $=\displaystyle \sqrt{0.2}=\sqrt{\frac{1}{5}}=\frac{\sqrt{5}}{5}$