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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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1 Answer

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.