Question

How do you convert `(5.7, -1.2)` into polar coordinates?

Answer 1

If `(x,y)` is are the coordinates of a point in the rectangular coordinate system then we convert it into polar form as follows.

Let the polar form of `(x,y)` be `(r,theta)`. Where `r` is the principal square root of sum of squares of the coordinates of the point in rectangular system i.e `r=sqrt(x^2+y^2)` and `theta` is the inverse tangent of the ratio from y coordinate to x coordinate in the rectangular coordinate system i.e `theta=tan^-1(y/x)`.
Here `x=5.7` and `y=-1.2`.
`implies r=sqrt((5.7)^2+(-1.2)^2)=sqrt(32.49+1.44)=sqrt33.93`
Also, `theta=tan^-1(-1.2/5.7)=tan^-1(-12/57)=tan^-1(-4/19)`.

Hence the polar form of the given number is `(sqrt33.93,tan^-1(-4/19))`.