Chapter 10.3, Problem 65E

To determine

To check: The correct option from the given options.

Answer to Problem 65E

The correct option is (C).

Explanation of Solution

Given information: It is given that for a point $a\ne 0$ and $\theta \ne 0$ .

Calculation:

Consider a point $\left(a,\theta \right)$ .

The directed negative distance of a point $-a$ in the $-\theta$ direction is the same as the directed positive distance $a$ in the $\theta$ direction.

So, the polar coordinates $\left(-a,-\theta \right)$ represent the same point.

The formula to find the other representation of a polar coordinates is given by $\left(r,\theta \right)=\left(r,\theta \pm 2n\pi \right)$ .

Substitute $a$ for $r$ and $1$ for $n$ in $\left(r,\theta -2n\pi \right)$ .

  $\left(r,\theta -2n\pi \right)=\left(a,\theta -2\pi \right)$

The polar coordinates given in option (A), (B) and (D) represent the same point.

Thus, the correct option is (C).