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I need help with a couple questions

1. What are the formulas used to convert a point from rectangular coordinates to polar coordinates?

2. How can you describe rectangular coordinates in terms of their polar counter parts?


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Pierce O. | Graduate Mathematics Student, Will Tutor Any Math SubjectGraduate Mathematics Student, Will Tutor...
4.7 4.7 (6 lesson ratings) (6)
Hi Raymond,
To convert from rectangular coordinates to polar coordinates, we use the following:
r = x2 + y2
θ = tan-1(y/x)
Given polar coordinates, we can find the rectangular coordinates as
x = r*cosθ
y = r*sinθ


One note about using the Θ = tan-1(y/x) formula. If x is 0, doing this with a calculator will cause an error because you can't divide by 0. You have to remember that if x is 0, your point must be on the y-axis, so your angle is either straight up (π/2 or 90°) or straight down (3π/2 or 270°). You can tell which one it is by checking whether y is positive or negative.