# What is the distance between the following polar coordinates?:  (12,(13pi)/8), (19,(-7pi)/8)

$d = \sqrt{505} = 22.47220505 \text{ }$units

#### Explanation:

Let ${r}_{1} = 12$ and ${r}_{2} = 19$ and Φ_2=(-7pi)/8 and Φ_1=(13pi)/8

The distance formula for polar coordinates

d = sqrt( r_1^2 + r_2^2 -2r_1r_2 cos(Φ_2 - Φ_1) )

$d = \sqrt{{12}^{2} + {19}^{2} - 2 \left(12\right) \left(19\right) \cdot \cos \left(\frac{- 7 \pi}{8} - \frac{13 \pi}{8}\right)}$

$d = \sqrt{505}$

$d = 22.47220505 \text{ }$units

God bless....I hope the explanation is useful.