Question

What is the distance between `(3 , (3 pi)/4 )` and `(9, pi )`?

Answer 1

`14.739`

Explanation:

`(r,theta)` in polar coordinates is `(rcostheta,rsintheta)` in rectangular coordinates.

Hence `(3,(3pi)/4)` is `(3cos((3pi)/4),3sin((3pi)/4))` or `(3*(-1)/sqrt2,3*(-1)/sqrt2)` or `((-3sqrt2)/2,-(3sqrt2)/2)`

and `9.pi)` is `(9cospi,9sinpi)` or `(9xx1,9xx0)` or `(9,0)`

The distance between `(9,0)` and `((-3sqrt2)/2,-(3sqrt2)/2)` is

`sqrt((9-((-3sqrt2)/2))^2+(0-((-3sqrt2)/2))^2)` or

`sqrt((9+(3sqrt2)/2)^2+((3sqrt2)/2)^2)` or

`sqrt(81+27sqrt2+9/2+9/2)` or

`sqrt(90+27sqrt2)` or `3sqrt(10+3sqrt2)` or

= `3sqrt(10+14.142)=3sqrt24.142=3xx4.913=14.739`