Question

What is the distance between `(-6 , (5 pi)/8 )` and `(3 , (5 pi )/3 )`?

Answer 1

≈3.1 ( 1 decimal place )

Explanation:

Use the Polar coordinate form of the distance formula which is :

`d^2 = r_1^2 + r_2^2 - (2 xxr_1 xx r_2 xx cos (theta_2 - theta_1 ))`

In this question let `(r_1 , theta_1 ) = (-6 , (5pi)/8 )` and

`( r_2 , theta_ 2) = (3 , (5pi)/3 )`

substitute values into formula :

`d^2 = (- 6 )^2 + 3^2 - ( 2 xx(-6) xx 3 xx cos ((5pi)/3 -(5pi)/8)`

`rArr d^2 = 36 + 9 - ( - 36 xx cos((25pi)/24) = 45 - ( 35.69)`

`d^2 = 9.31 rArr d = sqrt9.31 ≈3.1`