Question

What is the distance between `(3 ,( pi)/4 )` and `(-2 , ( pi )/2 )`?

Answer 1

`D=+-sqrt(13+6sqrt(2))` or `D~~+-4.64`

Explanation:

You are given two points in polar coordinates

• `(3,pi"/"4)` where `r_1=3` and `theta_1=pi"/"4`
• `(-2,pi"/"2)` where `r_2=-2` and `theta_2=pi"/"2`

The distance formula for polar coordinates is

`D^2=r_1^2+r_2^2-2*r_1*r_2*cos(theta_2-theta_1)`

Plug in the values above

`D^2=3^2+(-2)^2-2(3)(-2)cos(pi"/"2-pi"/"4)`
`D^2=9+4+12cos(pi"/"4)`
`D^2=13+12(sqrt(2)/2)`
`D^2=13+6sqrt(2)`

Now take the square root of both sides

`D=+-sqrt(13+6sqrt(2))`
`D~~+-4.64`