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Chapter 6: Problem 90

If you are given polar coordinates of a point, explain how to find two additional sets of polar coordinates for the point.

Short Answer

Expert verified
Given polar coordinates (r,胃), two additional sets of polar coordinates can be found as (-r, 胃+蟺) and (r, 胃+2蟺).

Step by step solution

01

Understanding polar coordinates

Given the polar coordinates (r, 胃), where r is the radial distance from the origin (distance from the point to the origin) and 胃 is the angle in standard position (angle counterclockwise from the positive x-axis), recall that there are infinite polar representations of the same point.
02

Finding additional polar coordinates

To get another two sets of polar coordinates, use the following operations: Consider (r, 胃), then to get new coordinates (-r, 胃+蟺) and (r, 胃+2蟺) where 蟺 is equivalent to 180掳 in degrees. The reasoning here is that adding 2蟺 to the angle gives a full turn in the plane, so the point is the same, and giving r a negative value while changing 胃 to 胃+蟺 makes r point in the opposite direction, again arriving at the same point.
03

Example illustration

For instance, if you are given a point with polar coordinates (2,蟺/4) the two additional sets of polar coordinates could be (-2, 5蟺/4) and (2, 9蟺/4).

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