Question

What is the distance between `(2 ,(7 pi)/6 )` and `(-7 , (5 pi )/4 )`?

Answer 1

`4sqrt5`

Explanation:

use the polar coordinate version of the distance formula

`d^2 = r_1^2 + r_2^2 - [2r_1r_2cos(theta_2 -theta_1) ]`

here let `(r_1,theta_1) = (2 ,(7pi)/6) , (r_2,theta_2) = (-7,(5pi)/4)`

substitute into formula

`d^2 = 2^2+(-7)^2 - [ 2 xx 2 xx(-7) xx cos((5pi)/4 - (7pi)/6)]`

`= 4 + 49 -[(-28 xx cos(pi/12) ]`

= 53 - (-27) = 80

`d^2 = 80 rArr d = sqrt80 =4sqrt5`