Question

What is the distance between the following polar coordinates?: `(7,(5pi)/4), (3,(13pi)/8)`

Answer 1

≈ 6.475

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)=(7,(5pi)/4)" and "(r_2,theta_2)=(3,(13pi)/8)`

`rArr d^2=7^2+3^2-[2xx7xx3cos((13pi)/8-(5pi)/4)]`

`d^2=49+9-(42cos((3pi)/8))`

`rArr d = sqrt(58 -42cos((3pi)/8)) ≈ 6.475`