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

You can use the fact that a full rotation is measured as 2π radians.

The correct answers are:

Option B:  (-r, theta + 3π)

Option C: (r, theta + 2π)

What is the measurement of full rotation?

When you rotate a full circle, then that is 2π radians sized angle.

When is an angle measured negative or positive?

When the rotation of terminal side (the moving side) of an angle occurs clockwise, then it is tagged with negative sign. If it moves counterclockwise, then it  is taken as a positive angle.

Getting same point as that with polar coordinates (r, theta)

Since theta + full rotation will land us again on that angle, thus we have:

 (r, theta)  denoting same point as  (r, theta + 2π)

There is a fact that if we negate(make negative) the radial coordinate and add 180 degrees or π radians (both measure same angle), then it represents same point in polar coordinate.

Thus, the point (r, theta + 2π) is same as  (-r, theta + 2π + π) = (-r, theta + 3π) (we negated the r and added 180 degrees or  π radians in angle)

Thus,

The correct answers are:

Option B:  (-r, theta + 3π)

Option C: (r, theta + 2π)

Learn more about polar coordinates here:

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