10.3 Parametric Equations & Polar Coordinates

Polar Coordinates

Question #1 (Easy): Plotting Polar Coordinates

Strategy

First draw the given polar coordinate. Get the angle right, then draw the r depending on the sign.

Then whether for , the key is to get the exact same line. It should make intuitive sense as the line

is drawn.

Sample Question

Plot the point of the polar coordinates. Then find two other pairs of polar coordinates of this point

where one has and the other with .

Solution

First start from the polar axis and go clockwise

since the angle given has negative sign. Then since r is

given as , from there flip degrees to the opposite side of the pole and draw length of .

Now, to have the exact same line with positive , can be kept at , but the angle would go

counterclockwise

. Thus the polar coordinate is then

which is equivalent to

Then to have negative r, the angle need to be aligned to

. There are many ways for this. Choosing

one counterclockwise would be

. Then the polar coordinate is then

which is also

given by

.

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