(Solved): Plot the point whose polar coordinates are given. Then find two other pairs of polar coordinate ...

Expert Answer

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Here we have to plot the point whose polar coordinates are given. Then find two other pairs of polar coordinates of this point, one with    and one with   .



To locate the point in the plane with polar coordinates (r,?) we imagine a ray from the origin that measures an angle of ? from the positive x-axis. Then we travel a distance of r along that ray if r>0 or along the opposite ray if r<0 and plot the point there.
Note that   

for any integer n because adding any multiple of 2? to ? gets us back to the same ray corresponding to ?.
Also,   .  we can change the sign of r by adding any multiple (including a negative multiple) of    to the angle to end up at the opposite angle. Then switching r to    we again end up at the same point.

(a). Given point   

For     

for      

Now we plot these points: