Question

How do you convert the rectangular coordinate `(-5,-5)` into polar coordinates?

Answer 1

The polar coordinates are `=(5sqrt2,(5pi)/4)`

Explanation:

If `(r,theta)` are the polar coordinates.
Then the equations of tranformation are
`x=rcostheta`
`y=rsintheta`
`r^2=x^2+y^2`
Here we have `(x,y)` `=(-5,-5)`
So `-5=rcostheta` and `-5=rsintheta`
Therefore, we are in the 3rd quadrant
`tantheta=1` ; `theta=(5pi)/4`
And `r^2=(-5)^2+(-5)^2=50`
so `r=sqrt50=5sqrt2`