Question

How do you convert `(-6,-3)` into polar coordinates?

Answer 1

Polar coordinates of `(−6,−3)` are `(3sqrt5, 206.565^o)`

Explanation:

If `(x, y)` are converted into polar coordinates `(r, theta)`,

while `(x, y)` in terms of `r` and `theta` are `x=rcostheta` and `y=rsintheta`, `(r, theta)` in terms of `x` and `y` are `r=sqrt(x^2+y^2)` and `theta=tan^-1(y/x)`

Hence, converting `(−6,−3)` into polar coordinates

`r=sqrt((-6)^2+(-3^2)` = `sqrt45` = `3sqrt5`

`theta=tan^-1((-3)/-6)` = `tan^-1(1/2)`. Further, as `(−6,−3)` is in third quadrant `theta=(180+26.565)=206.565^o`

Hence polar coordinates of `(−6,−3)` are `(3sqrt5, 206.565^o)`