What is the distance between the following polar coordinates?: (16,19π12),(11,17π8)

1 Answer
May 9, 2016

Distance between the polar coordinates is 20.566

Explanation:

A polar coordinate (r,θ) is (rcosθ,rsinθ) in Caresian coordinates.

Hence (16,19π12) is (16cos(19π)12,16sin(19π)12) or (16×0.2588,16×0.9659) or (4.1408,15.4544)

(11,17π8) is (11cos(17π)8,11sin(7π)8) or (11×0.9239,11×0.3827) or (10.1629,4.2097)

Hence distance between two points is given by (10.16294.1408)2+(4.2097+15.4544)2 or

6.02212+19.66412

= 36.2657+386.6768

= 422.9425=20.566