Question

If r cannot equal 0, which of the following polar coordinate pairs represents the same point as the point with polar coordinates (r, theta) select all that apply (2 correct answers)
a. (-r, theta - 2π)
b. (-r, theta + 3π)
c. (r, theta + 2π)
d. (r, theta - π)

Answer 1

In rectangular coordinates, the coordinates of (r, theta) are (r cos theta, r sin theta).  Adding pi to theta reflects (sin theta, cos theta) across (0, 0).  Multiplying r by -1 does so as well, so b will have no effect (as these effects cancel out).  Adding a multiple of 2pi has no effect, so c has no effect either.  The other two reflect (r, theta) across (0, 0), so they are not valid options.  Thus, b and c are the answers.