# What is the distance between the following polar coordinates?:  (16,(19pi)/12), (11,(17pi)/8)

May 9, 2016

Distance between the polar coordinates is $20.566$

#### Explanation:

A polar coordinate $\left(r , \theta\right)$ is $\left(r \cos \theta , r \sin \theta\right)$ in Caresian coordinates.

Hence $\left(16 , \frac{19 \pi}{12}\right)$ is $\left(16 \cos \frac{19 \pi}{12} , 16 \sin \frac{19 \pi}{12}\right)$ or $\left(16 \times 0.2588 , 16 \times - 0.9659\right)$ or $\left(4.1408 , - 15.4544\right)$

$\left(11 , \frac{17 \pi}{8}\right)$ is $\left(11 \cos \frac{17 \pi}{8} , 11 \sin \frac{7 \pi}{8}\right)$ or $\left(11 \times 0.9239 , 11 \times 0.3827\right)$ or $\left(10.1629 , 4.2097\right)$

Hence distance between two points is given by $\sqrt{{\left(10.1629 - 4.1408\right)}^{2} + {\left(4.2097 + 15.4544\right)}^{2}}$ or

$\sqrt{{6.0221}^{2} + {19.6641}^{2}}$

= $\sqrt{36.2657 + 386.6768}$

= $\sqrt{422.9425} = 20.566$