# What is the distance between the following polar coordinates?:  (1,(-5pi)/12), (5,(11pi)/8)

Oct 15, 2017

Distance = 5.0206

#### Explanation:

Distance between two points with polar coordinates :
$d = \sqrt{r {1}^{2} + r {2}^{2} - 2 r 1 r 2 \left(\cos \left(\theta 1 - \theta 2\right)\right)}$
Given
${r}_{1} = 1 , {r}_{2} = 5 , {\theta}_{1} = - \left(\frac{5 \pi}{2}\right) , {\theta}_{2} = \frac{11 \pi}{2}$
d = sqrt(1 + 25 - (2*1*5*(cos ((-5pi)/12)-((11pi)/8))
 = sqrt(26- 10 cos(-(43pi)/24)
 = sqrt (26-10cos((43pi)/24)) = sqrt(26 - 10*0.7934
$d = \sqrt{25.2066} = 5.0206$