How it works ?
Recall that the polar coordinates of a certain location (i.e. point) in the coordinate plane are NOT UNIQUE. Unlike rectangular coordinates, there are INFINITELY MANY POLAR COORDINATE REPRESENTATIONS of a point plotted in the coordinate plane.
In the applet below, a point is given in polar coordinates. Your job is simply to write a different pair of polar coordinates so that these coordinates yield the same location as the given ordered pair. (If you type in a correct pair of polar coordinates, the applet will indicate this to you.)
When inputting your data, use “pi” for “pi” (the symbol browser isn’t working here.)
Try inputting a few ordered pairs for each problem you generate.
As you do, try writing at least 2 ordered pairs with r < 0 and at least 2 ordered pairs with r > 0.
Also try writing at least 2 ordered pairs with theta > 0 and at least 2 ordered pairs with theta < 0.
Generate as many practice problems as you need in order to master this concept!