text: # Precalculus : Convert Rectangular Coordinates To Polar Coordinates and vice versa
  
  ## Example Questions
  
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  ### Example Question #75 : Polar Coordinates
  
  Which polar-coordinate point is not the same as the rectangular point ?
  
  Explanation:
  
  Plotting this point creates a triangle in quadrant I:
  
  Using our knowledge of Special Right Triangles, we can conclude that the angle is and the radius/hypotenuse of this triangle is . Our polar coordinates are therefore , so we can eliminate that as a choice since we know it works.
  
  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 would correspond with our angle of , so  works.
  
  We can see that if our radius is negative we'd want to start off at the angle , so the point  works.
  
  As we can see from looking at this excerpt from the unit circle, another way of writing the angle would be to write , so the point  works.
  
  The only one that does not work would be  because that would place us in quadrant II rather than I like we want.
  
  ### Example Question #76 : Polar Coordinates
  
  Which of the following is a set of polar coordinates for the point with the rectangular coordinates
  
  Explanation:
  
  The relation between polar coordinates and rectangular coordinates is given by  and .
  
  You can plug in each of the choices for  and  and see which pair gives the rectangular coordinate .
  
  The answer turns out to be .
  
  Alternatively, you can find  by the equation
  
  , thus
  
  .
  
  As for finding , you can use the equation
  
  , and since
  
  .
  
  Thus, the polar coordinate is
  
  ### Example Question #77 : Polar Coordinates
  
  Convert the point to polar form
  
  Explanation:
  
  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 #78 : Polar Coordinates
  
  Convert the following rectangular coordinates to polar coordinates:
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