Chapter 5 - Trigonometric Identities - Section 5.6 Half-Angle Identities - 5.6 Exercises - Page 243: 61

$$m=2$$

$$\sin\frac{\theta}{2}=\frac{1}{m}$$ $$\theta=60^\circ$$ In this exercise, it is much faster and easier to replace the angle into the formula right away. $$\sin\frac{60^\circ}{2}=\frac{1}{m}$$ $$\sin30^\circ=\frac{1}{m}$$ $$\frac{1}{2}=\frac{1}{m}$$ $$m=2$$ $m=2$ is the final result.