# What is the distance between the following polar coordinates?:  (2,(7pi)/12), (1,(2pi)/12)

Apr 8, 2016

${P}_{1} {P}_{2} = \sqrt{3.96472382} \approx 1.99$

#### Explanation:

Distance Formula in Polar Plane: ${P}_{1} {P}_{2} = \sqrt{{r}_{1}^{2} + {r}_{2}^{2} - 2 {r}_{1} {r}_{2} \cos \left({\theta}_{2} - {\theta}_{1}\right)}$

${r}_{1} = 2 , {\theta}_{1} = \frac{7 \pi}{12} , {r}_{2} = 1 , {\theta}_{2} = \frac{2 \pi}{12}$

${P}_{1} {P}_{2} = \sqrt{{2}^{2} + {1}^{2} - 2 \left(2\right) \left(1\right) \cos \left(\frac{2 \pi}{12} - \frac{7 \pi}{12}\right)}$

${P}_{1} {P}_{2} = \sqrt{4 + 1 - 4 \cos \left(- \frac{5 \pi}{12}\right)}$

${P}_{1} {P}_{2} = \sqrt{5 - 4 \cos \left(\frac{5 \pi}{12}\right)}$

${P}_{1} {P}_{2} = \sqrt{3.96472382} \approx 1.99$