Chapter 5 - Section 5.3 - Double-Angle, Power-Reducing, and Half-Angle Formulas - Exercise Set - Page 682: 79

a. $d=\frac{v_0^2}{32}sin2\theta$ b. $\theta=\frac{\pi}{4}$ or $45^\circ$

a. Using the identity $2sin\theta cos\theta = sin2\theta$, we can write the equation as $d=\frac{v_0^2}{32}sin2\theta$ b. For a maximum $d$, we have $sin2\theta=1$, $2\theta=\frac{\pi}{2}$, and $\theta=\frac{\pi}{4}$ or $45^\circ$