Question

What is the distance between `(2 ,(5 pi)/6 )` and `(5 , (7 pi )/12 )`?

Answer 1

≈ 3.855 units

Explanation:

Using the`color(blue)" Polar version of the distance formula "`

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

let`(r_1,theta_1)=(2,(5pi)/6)" and " (r_2,theta_2)= (5,(7pi)/12)`

`d^2 =2^2+5^2-(2xx2xx5cos[(7pi)/12)-((5pi)/6)]`

`= 4+25 - ( 20cos(-pi/4) = 29 - 20cos(-pi/4) ≈ 14.8578`

`rArr d^2 ≈ 14.8578 rArr d = sqrt14.8578 ≈ 3.855`