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May 16th, 2017, 12:42 PM   #1
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A question about converting cylindrical coordinates to rectangular coordinates

I have a problem figuring something out when it comes to converting cylindrical to 3D rectangular coordinates.

the formulas for converting are as follows:

x = r cos theta
y = r sin theta
z = z

If we're just using basic trigonometry to figure out the sides of the triangle of which the angle theta is a part of, and the angle itself lies between x and r, how can we use any of these functions to figure out the y if y is not a part of the same triangle with x and r? Shouldn't the angle between r and y be something other than theta ? How can we get y by applying these functions to theta then? Can anyone please explain this?

Thanks.

Last edited by skipjack; May 17th, 2017 at 06:17 AM.
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May 19th, 2017, 03:28 AM   #2
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I don't understand how it could possibly happen that "y is not a part of the same triangle with x and r". "r" is, by definition of "polar" (and so "cylindrical") coordinates, the line from the origin to the point (x, y). It is always the hypotenuse of a right triangle having x and y as legs.
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