## Trigonometry (11th Edition) Clone

Arc length s (for central angle $\theta$):$\quad s=r\theta$, where $\theta$ is in radians Converting between Degrees and Radians 1. Multiply a degree measure by $\displaystyle \frac{\pi}{180}$ radian and simplify to convert to radians. 2. Multiply a radian measure by $\displaystyle \frac{180^{\mathrm{o}}}{\pi}$ and simplify to convert to degrees. ---------------- For the smaller gear, the length of the arc that turns is $s=r\theta$ $\theta=120^{o}$ needs to be converted to radians (case 1): $s=r\displaystyle \cdot 120\cdot\frac{\pi}{180}=14.6\cdot 2\cdot\frac{\pi}{3}=\frac{29.2\cdot\pi}{3}$ This arc length is the same as the arc length of the larger wheel, rotating through the angle of $60.0^{o}.$ $s=r\theta\qquad$ ( ... solve for $r$) $\theta = 60.0\displaystyle \cdot\frac{\pi}{180}=\frac{\pi}{3}$ radians $\displaystyle \frac{29.2\cdot\pi}{3}=r\cdot\frac{\pi}{3}$ $r=\displaystyle \frac{29.2\cdot\pi\cdot 3}{3\cdot\pi}=$29.2 The radius of the bigger wheel is 29.2 in.