Question

What is the distance between the following polar coordinates?: `(3,(-5pi)/12), (6,(3pi)/8)`

Answer 1

`8.576" " "units"`

Explanation:

First find the respective `x` and `y`

1st Point:
`x=r cos(theta)=3 cos((-5pi)/12)=0.7765`
`y= sin(theta)= 3 sin((-5pi)/12)=-2.8978`

2nd Point:
`x=6 cos((3pi)/8)=2.2961`
`y=6 sin((3pi)/8)=5.5432`

Solve for the distance:
`d=sqrt((x_1-x_2)^2+(y_1-y_2)^2)`
`d=sqrt((0.7765-2.2961)^2+(-2.8978-5.5432)^2)`
`d=sqrt(2.3092+71.2505)`
`d=sqrt(73.5597)`
`d=8.576`