View source for Intuitive Trigonometry/Appendix 1: Solutions to Problems

==Appendix 1: Solutions to Problems==
===Radians and Arc Length===
# <math>\ell_{\text{arc}}=2\pi r\left(\frac{\theta}{360^{\circ}}\right)</math> is our formula for arc length; we can plug in our given values and solve. <math>\ell=2\pi\times 2\left(\frac{10^{\circ}}{360^{\circ}}\right)</math> which simplifies to <math>\ell=\frac{4\pi}{36}</math> (notice the degree signs cancel) and further simplifies to <math>\ell=\frac{\pi}{9}</math> which is our solution.
# <math>2\pi\text{ rad}=360^{\circ}</math>, so we can create a proportion 
# <math>2\pi\text{ rad}=360^{\circ}</math>, so we can create a proportion
# <math>\ell_{\text{arc}}=2\pi r\left(\frac{\theta}{360^{\circ}}\right)</math> is our formula for arc length; we can plug in our given values and solve. <math>5=2\pi\times 4\left(\frac{\theta}{360^{\circ}}\right)</math> which simplifies to <math>5=\frac{8\pi\theta}{360^{\circ}}</math> or <math>1800^{\circ}=8\pi\theta</math> or <math>\frac{1800}{8\pi}^{\circ}=\frac{225}{\pi}^{\circ}=\theta</math>, which is our solution.
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{{Intuitive Trigonometry}}