Question

What is the distance between `(2 ,(5 pi)/4 )` and `(8 , (11 pi )/12 )`?

Answer 1

`7.211`

Explanation:

`(2,(5pi)/4)` in rectangular coordinates would be `(2cos((5pi)/4), 2sin((5pi)/4))`. As `sin((5pi)/4)=-sqrt2/2` and `cos((5pi)/4)=-sqrt2/2`

This is `(-sqrt2,-sqrt2)` or `(-1.4142,-1.4142)`.

`(8,(11pi)/12)` in rectangular coordinates would be `(8cos((11pi)/12), 8sin((11pi)/12))`. As `sin((11pi)/12)=0.2588` and `cos((5pi)/4)=-0.9659`

This is `(-7.7272,2.0704)`.

Hence distance between two is `sqrt{((-7.7272-(-1.4142))^2+((2.0704-(-1.4142))^2`

= `sqrt{(6.313)^2+(3.4846)^2}=sqrt51.9964=7.211`