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May 16th, 2017, 12:03 PM   #1
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A question about cylindrical coordinates

So cylindrical coordinates are basically a 3D representation of polar coordinates. Since with polar coordinates we can use basic trigonometry to figure out the length of the triangle sides x or y and therefore convert from polar to 2D rectangular, the same is true for converting from cylindrical to 3D rectangular.

The formulas for converting cylindrical to 3D rectangular are :
x = r cos theta
y = r sin theta
z = z

Now, my questions is: WHY is y = r sin theta ?

If theta is the angle between x and r , why is it applicable to y? Am I looking at this the wrong way? The way I see it, y isn't even part of the triangle that contains the theta angle. When looking for cos theta , we get it by dividing it's adjacent side (x) with the hypotenuse (r) . But when looking for sin theta, shouldn't the opposite side we need in the equation be a line drawn between x and r ?

When I can't figure something like this out it just keeps bugging me and I can't move on with the materia and just apply the formula. Can anyone help clear this up?
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