# Intuitive Trigonometry/Appendix 1: Solutions to Problems

## Appendix 1: Solutions to Problems

1. $\ell _{\text{arc}}=2\pi r\left({\frac {\theta }{360^{\circ }}}\right)$  is our formula for arc length; we can plug in our given values and solve. $\ell =2\pi \times 2\left({\frac {10^{\circ }}{360^{\circ }}}\right)$  which simplifies to $\ell ={\frac {4\pi }{36}}$  (notice the degree signs cancel) and further simplifies to $\ell ={\frac {\pi }{9}}$  which is our solution.
2. $2\pi {\text{ rad}}=360^{\circ }$ , so we can create a proportion
3. $2\pi {\text{ rad}}=360^{\circ }$ , so we can create a proportion
4. $\ell _{\text{arc}}=2\pi r\left({\frac {\theta }{360^{\circ }}}\right)$  is our formula for arc length; we can plug in our given values and solve. $5=2\pi \times 4\left({\frac {\theta }{360^{\circ }}}\right)$  which simplifies to $5={\frac {8\pi \theta }{360^{\circ }}}$  or $1800^{\circ }=8\pi \theta$  or ${\frac {1800}{8\pi }}^{\circ }={\frac {225}{\pi }}^{\circ }=\theta$ , which is our solution.