# Chapter 5 - Section 5.5 - Trigonometric Equations - Exercise Set - Page 705: 136

$26^\circ, 64^\circ$

#### Work Step by Step

Step 1. Given the model function $d=\frac{v^2_0}{16}\ sin\theta\ cos\theta$, with $v_0=90\ ft/sec$ and $d=200\ ft$, we have $\frac{90^2}{16}\ sin\theta\ cos\theta=200$ or $sin(2\theta)=0.7901$ Step 2. With $sin^{-1}(0.7901)\approx52^\circ$, the general solutions for the above equation are $2\theta=360^\circ k+52^\circ$ and $2\theta=360^\circ k+180^\circ-52^\circ$, which gives $\theta=180^\circ k+26^\circ$ and $\theta=180^\circ k+64^\circ$ where $k$ is an integer. Step 3. Within $(0^\circ,90^\circ)$, we have $\theta=26^\circ, 64^\circ$

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