Precalculus : Convert Rectangular Coordinates To Polar Coordinates and vice versa
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Example Questions
Example Question #21 : Convert Rectangular Coordinates To Polar Coordinates And Vice Versa
Which polar-coordinate point is not the same as the rectangular point 
Plotting this point creates a triangle in quadrant I:
Using our knowledge of Special Right Triangles, we can conclude that the angle is 
Looking at the unit circle [or just the relevant parts] can give us a sense of what happens when the angles and/or the radii are negative:
Now we can easily see that the angle 
We can see that if our radius is negative we'd want to start off at the angle 
As we can see from looking at this excerpt from the unit circle, another way of writing the angle 
The only one that does not work would be 
Example Question #72 : Polar Coordinates
Which of the following is a set of polar coordinates for the point with the rectangular coordinates 
The relation between polar coordinates and rectangular coordinates is given by 
You can plug in each of the choices for 
The answer turns out to be 
Alternatively, you can find 
As for finding 
Thus, the polar coordinate is 
Example Question #71 : Polar Coordinates
Convert the point 
First, find r using pythagorean theorem,
Then we can find theta by doing the inverse tangent of y over x:
Since this point is in quadrant II, add 180 degrees to get
Example Question #1671 : Pre Calculus
Convert the following rectangular coordinates to polar coordinates:
To convert from rectangular coordinates to polar coordinates 
Using the rectangular coordinates given by the question,
The polar coordinates are
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