Q. 3 - Calculus

Question

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

Step-by-Step Solution

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 1: 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.

Step 2: 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 $x$-axis, so by adding an integer rotation of $2\pi$ does not change the location of the point.

Hence the explanation.