Question

What is the distance between the following polar coordinates?: `(1,(pi)/4), (12,(9pi)/8)`

Answer 1

Distance `color(red)(d=12.92954402832" ")`units

Explanation:

Distance between two polar coordinates formula

`d=sqrt(r_1^2+r_2^2-2*r_1*r_2*cos (theta_2-theta_1)`

Solution:
Let `(r_1, theta_1)=(1, pi/4)`
Let `(r_2, theta_2)=(12, (9pi)/8)`

Use
`d=sqrt(r_1^2+r_2^2-2*r_1*r_2*cos (theta_2-theta_1)`
`d=sqrt(1^2+12^2-2*(1)*(12)*cos ((9pi)/8-pi/4)`
`d=sqrt(145-24*cos ((7pi)/8))`
`color(red)(d=12.92954402832" ")`units

God bless....I hope the explanation is useful.