Chapter 11.3, Problem 65E

To determine

To determine: The correct answer for the exceptional ordered pair which does not represent the same point in polar coordinates if $a\ne 0$ and $\theta \ne 0$ .

Answer to Problem 65E

The correct answer is (B).

Explanation of Solution

Given information:

The options:

(A) $\left(a,\theta \right)$

(B) $\left(-a,-\theta \right)$

(C) $\left(-a,\theta -\pi \right)$

(D) $\left(-a,\theta +\pi \right)$

(E) $\left(a,\theta -2\pi \right)$

Calculation:

It is seen that $\left(r,\theta \right)$ is the point which has the distance from the pole that is, r and the angle made by the line with the positive x -axis that is, $\theta$ .

This means that the ordered pairs $\left(a,\theta \right)$ , $\left(-a,\theta -\pi \right)$ , $\left(-a,\theta +\pi \right)$ and $\left(a,\theta -2\pi \right)$ represent the same point and the ordered pair $\left(-a,-\theta \right)$ does not represent the same point.

Hence, the correct answer is (B).