Question

What are the polar coordinates of A? Give an exact answer.

Answer 1

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,

`(r,\theta)`

where r is the distance of the point from the pole, and θ is the measure of the angle.

we know that,

`r^2=x^2+y^2`
`\theta=tan^(-1)((y)/(x))`

we get,

(x,y)=(6,-6)

x=6, y=-6

Using this we get,

`r^2=6^2+(-6)^2`
`r^2=36+36`
`r^2=72`
`r=8.48`

Then,

`\theta=tan^(-1)((-6)/(6))`

`\theta=tan^(-1)(-1)`
`\theta=-(\pi)/(4)`

we get the polar coordinate of A is,

`(r,\theta)=(8.48,-(\pi)/(4))`