Question

What is the polar form of `( -51,6 )`?

Answer 1

Polar form coordinates are `(3sqrt293,173.29^o)`

Explanation:

A rectangular coordinate `(x,y)` can be written as polar coordinate `(r,theta)`, where `x=rcostheta`, `y=rsintheta`, `theta=tan^(-1)(y/x)` and `r=sqrt(x^2+y^2)`.

As we have rectangular coordinate `(-51,6)`

`r=sqrt((-51)^2+6^2)=sqrt(2601+36)sqr2637=3sqrt293`

and `theta=tan^(-1)(-6/51)=tan^(-1)(-0.11765)=(180-6.71)^o=173.29^o`

Note - As `tantheta` is negative and while `costheta` is negative and `sintheta` is positive, we have taken `theta` in second quadrant.

Hence polar form coordinates are `(3sqrt293,173.29^o)`