Question

What is the polar form of `( -1,-2 )`?

Answer 1

polar coordinate `(sqrt5,tan^-1 2)`

Explanation:

`x= rcos theta and y =rsintheta`
here `x = -1 and y = -2`
the point is in third quadrant
So`tantheta = y/x=(-2)/-1=2`
as the point is in 3rd coordinate
`:. theta = pi+tan^-1 2`
and `r = sqrt(x^2+y^2)=sqrt5`

polar coordinate `(sqrt5,pi+tan^-1 2)`

Answer 2

`(sqrt5, pi+tan^(-1)2)`

Explanation:

The equations `x = -1 = r cos theta and y = -2 = r sin theta` give
r = `sqrt(x^2+y^2)=sqrt5`.

To find `theta`, observe that both `sin theta` and `cos theta` are negative. The angle is in the third quadrant. The first quadrant angle `theta=tan^(-1)2`. The angle for the opposite direction is the correct value for `theta`.i

`tan (pi+theta) = tan theta`
So, `theta=pi+tan^(-1)2`. .