Question

What is the distance between the following polar coordinates?: `(2,(pi)/2), (2,(17pi)/12)`

Answer 1

`bar(AB)\approx3.9658`

Explanation:

Graph the two points:

A triangle is formed when the two points `A` and `B` are connected to the origin `O`. We know the angle `/_AOB` is `(17pi)/12-pi/2=(11pi)/12`, and the two sides `bar(AO)=bar(BO)=2`.

Then, `bar(AB)` can be found using the law of cosines:
`bar(AB)^2=bar(AO)^2+bar(BO)^2-2*bar(AO)*bar(BO)*cos(/_AOB)`
`bar(AB)^2=2^2+2^2-2*2*2*cos((11pi)/12)`
`bar(AB)^2\approx15.7274`

`thereforebar(AB)\approx3.9658`