Question

What is the distance between the following polar coordinates?: `(6,(17pi)/12), (5,(9pi)/8)`

Answer 1

1. They have different radii
2. They have different angles

Explanation:

Polar coordinates are written in the following format:
`(r,\theta )`
Where `r` is the distance from the origin and `\theta` is the angle rotated counterclockwise about the origin from the x-axis. You can convert to polar coordinates by using the following formulas.
`x=rcos(\theta)`
`y=rsin(\theta)`
`tan(\theta)=\frac{y}{x}`
If you plot your points in either Cartesian or polar coordinates, you can clearly see the difference.

Answer 2

`"Distance "approx 10.42119`

Explanation:

`(6,frac{17pi}{12}),(5,frac{5pi}{8})`

Convert to Cartesian coordinates, remember the following formulas:
`color(red)(x=rcostheta)`
`color(red)(y=rsintheta)`

First coordinate: `(6,frac{17pi}{12})`
`x=6cos((17pi)/12)`

`y=6sin((17pi)/12)`

`color(blue)((6cos((17pi)/12),6sin((17pi)/12))`

Second coordinate: `(5,frac{5pi}{8})`
`x=5cos((5pi)/8)`

`y=5sin((5pi)/8)`

`color(blue)((5cos((5pi)/8),5sin((5pi)/8))`

Use the distance formula (Pythagorean Theorem) between these points:
`"Distance"=sqrt((6cos((17pi)/12)-5cos((5pi)/8))^2+(6sin((17pi)/12)-5sin((5pi)/8))^2)`

`"Distance "approx 10.42119`