Question

How do you convert `(-3,3)` to polar form?

Answer 1

`(3sqrt2,3pi/4)`

Explanation:

If Cartesian coordinate of point is (x,y)
and its polar coordinate is `(r,theta)`
then `x=rcostheta`and `y=rsintheta`
given x= -3 then `-3=rcostheta`
and y= 3 ,So `3=rsintheta`
`tantheta=-1`
both `tantheta ,costheta` are negative and`sin theta` is poitive So the angle`theta` will be in 2nd quadrant
Hence`theta =pi-pi/4=3pi/4`
`r^2= 3^2+(-3)^2`
`r=3sqrt2`
hence reqd polar coordinate is`(3sqrt2,3pi/4)`