Question

Explain why every point in the polar coordinate plane has infinitely many different polar coordinate representations.

Short answer

The value of $\theta$in the polar coordinate for a point $p$ measures the angular rotation of $p$ from the $x$-axis, so by adding an integer rotation of $2\pi$ does not change the location of the point.

Hence the explanation.

Step-by-step solution

Given information

Every point in the polar coordinate plane has infinitely many different polar coordinate representations. Polar coordinates are pair of numbers used to describe the position of a point in a plane.

Simplification

Polar coordinates are pair of numbers used to describe the position of a point in a plane.

They are denoted by $(r,\theta )$. Where $\theta$is the directed angular measure in radians and $r$is the directed distance from the origin or pole.

When $\theta >0$, we rotate counterclockwise from the polar axis, and when $\theta <0$we rotate clockwise. when $r>0$, we measure $r$units along the ray specified by the value of $\theta$. When $r<0$,we measure $\left|r\right|$units in the opposite direction.

The value of $\theta$in the polar coordinate for a point $p$measures the angular rotation of $p$from the localid="1652104868402" $x$-axis, so by adding an integer rotation of $2\pi$ does not change the location of the point.

Hence the explanation.