Question

For the given point in rectangular coordinates, how do you find the corresponding polar coordinates for the point `(10 sqrt (3), 10)`?

Answer 1

`(20,pi/6)`

Explanation:

To convert from (x ,y) to `(r,theta)` use the formulae which connect Cartesian to Polar coordinates.

`•r=sqrt(x^2+y^2)`

`•theta=tan^-1(y/x)`

here x`=10sqrt3" and "y=10`

`rArrr=sqrt((10sqrt3)^2+10^2)=sqrt(300+100)=sqrt400=20`

and `theta=tan^-1(10/(10sqrt3))=tan^-1(1/sqrt3)=pi/6`

`rArr(10sqrt3,10)→(20,pi/6)`