Question

What is the polar form of `(-2,10)`?

Answer 1

`r=sqrt(x^2+y^2 ) =sqrt(4+100)=sqrt 104=2 sqrt 26`
`theta=tan^-1 (y/x)=tan^-1 (10/-2) = (tan^-1 -5) =-1.373...->pi-1.373...or -1.373...+pi->theta ~~1.768 -> (2 sqrt 26 , 1.768)`

Explanation:

Use the formulas `r^2=x^2+y^2 and tan theta = y/x`to change the point from rectangular to polar. Note that the point (-2,10) is in quadrant 2 hence to find `theta` we have to add `pi` or 180 to the negative answer we got or ignore the negative sign and subtract from `pi`