Question

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

Answer 1

≈ 3.98 units

Explanation:

To calculate the distance between 2 polar coordinate points , use the `color(blue)(" Polar 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) " and" (r_2,theta_2) = (-4,(7pi)/4)`

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

`= 4 + 16 - (-16cos((7pi)/12))= 20 - ( 4.144) = 15.856`

`rArr d^2 = 15.856 rArr d = sqrt15.856 ≈ 3.98`