Answer:
To find coordinate of A, it is (6,-6) in polar coordinate.
we know that,
The polar coordinate system as a method in which a point is described by its distance from a fixed point at the center of the coordinate space known as a pole and by the measurement of the angle formed by a fixed-line and a line from the pole through the given point.
In the polar coordinate system, the coordinates of a point are represented as,
[tex](r,\theta)[/tex]
where r is the distance of the point from the pole, and θ is the measure of the angle.
we know that,
[tex]r^2=x^2+y^2[/tex][tex]\theta=tan^{-1}(\frac{y}{x})[/tex]
we get,
(x,y)=(6,-6)
x=6, y=-6
Using this we get,
[tex]r^2=6^2+(-6)^2[/tex][tex]r^2=36+36[/tex][tex]r^2=72[/tex][tex]r=8.48[/tex]
Then,
[tex]\theta=tan^{-1}(\frac{-6}{6})[/tex]
[tex]\theta=tan^{-1}(-1)[/tex][tex]\theta=-\frac{\pi}{4}[/tex]
we get the polar coordinate of A is,
[tex](r,\theta)=(8.48,-\frac{\pi}{4})[/tex]
