Question

What is the distance between `(4 , pi/12 )` and `(5, pi/12 )`?

Answer 1

`1`

Explanation:

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

Hence, `(4,pi/12)` in rectangular coordinates is

`(4cos(pi/12),4sin(pi/12))` or

`(4xx0.9659,4xx0.2588)` or `(3.8636,1.0352)`

And, `(5,pi/12)` in rectangular coordinates is

`(5cos(pi/12),5sin(pi/12))` or

`(5xx0.9659,5xx0.2588)` or `(4.8295,1.294)`

The distance between the two points is `sqrt((4.8295-3.8636)^2+(1.294-1.0352)^2)` or `sqrt((0.9659)^2+(0.2588)^2)` or `sqrt(0.93296281+0.06697744)` or `sqrt(0.99994025)=1`

Actually the distance will be exactly `1` as both points have same `theta` coordinate, bur difference between `r` coordinate is exactly `1`. Minor difference has arisen because of rounding of numbers.