Chapter 7 - 7.5 - Multiple-Angle and Product-to-Sum Formulas - 7.5 Exercises - Page 549: 73

$x=2r(1-cos~θ)$

Power Reducing Formula (page 543): $sin^2x=\frac{1-cos~2x}{2}$ Now, make $x=\frac{θ}{2}$: $sin^2\frac{θ}{2}=\frac{1-cos~θ}{2}$ $\frac{x}{2}=2r~sin^2\frac{θ}{2}$ $\frac{x}{2}=2r~\frac{1-cos~θ}{2}$ $\frac{x}{2}=r(1-cos~θ)$ $x=2r(1-cos~θ)$