# What is the distance between the following polar coordinates?:  (5,(3pi)/4), (1,(9pi)/8)

Dec 22, 2017

Distance between the polar coordinates is $4.71$

#### Explanation:

The polar coordinates $\left(5 , \frac{3 \pi}{4}\right)$ and $\left(1 , \frac{9 \pi}{8}\right)$

in rectangular coordinates are

(5cos((3p)/4),5sin((3p)/4) i.e. $\left(- \frac{5}{\sqrt{2}} , \frac{5}{\sqrt{2}}\right)$ or $\left(- 3.5355 , 3.5355\right)$

and $\left(\cos \left(\frac{9 p}{8}\right) , \sin \left(\frac{9 p}{8}\right)\right)$ i.e. $\left(- 0.9239 , - 0.3827\right)$

Hence distance between two is

$\sqrt{{\left(- 3.5355 + 0.9239\right)}^{2} + {\left(3.5355 + 0.3827\right)}^{2}}$

= $\sqrt{{2.6116}^{2} + {3.9182}^{2}}$

= $\sqrt{6.82045456 + 15.35229124}$

= $\sqrt{22.1727458}$

= $4.71$