# What is the distance between (2 ,(7 pi)/6 ) and (2 , (5 pi )/12 )?

Mar 28, 2016

$s = 3 , 695 \text{ unit}$

#### Explanation:

$\text{ distance between two point which given at polar form:}$
$s = \sqrt{{r}_{1}^{2} + {r}_{2}^{2} - 2 \cdot {r}_{1} \cdot {r}_{2} \cdot \cos \left({\theta}_{2} - {\theta}_{1}\right)}$
${P}_{1} = \left({r}_{1} , {\theta}_{1}\right) \text{ Point } {P}_{1}$
${P}_{2} = \left({r}_{2} , {\theta}_{2}\right) \text{ Point } {P}_{2}$
${P}_{1} = \left(2 , \frac{7 \pi}{6}\right)$
${P}_{2} = \left(2 , \frac{5 \pi}{12}\right)$
${r}_{1} = 2$
${r}_{2} = 2$
${\theta}_{1} = \frac{7 \pi}{6}$
${\theta}_{2} = \frac{5 \pi}{12}$

${\theta}_{2} - {\theta}_{1} = \frac{5 \pi}{12} - \frac{7 \pi}{6}$
${\theta}_{2} - {\theta}_{1} = \frac{5 \pi - 14 \pi}{12}$

${\theta}_{2} - {\theta}_{1} = - \frac{9 \pi}{12}$
$\cos \left(- \frac{9 \pi}{12}\right) = - 0 , 707$
$s = \sqrt{{2}^{2} + {2}^{2} - 2 \cdot 2 \cdot 2 \cdot \left(- 0 , 707\right)}$
s=sqrt(4+4+8*0,707
$s = \sqrt{8 + 5 , 656}$
$s = \sqrt{13 , 656}$
$s = 3 , 695 \text{ unit}$