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Converting between 2D Polar and Cartesian

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I am having a bit of struggle getting to grips with this. I have had a look on google but failed to find anything suffecient to break this down into absolute basics with pretty diagrams. Anyone know of any resources for this exact thing or anyone have any pretty diagrams and basic explanations? Help appreciated as I am far far far from being a math guru

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In 2D it´s quite easy to draw a small diagram yourself. Draw your two axes and a circle with radius r around the origin of your coordiante system. Then, choose any point on your circle (chosing one in the upper right quarter might simplify things at first). Draw a connection line from the origin to that point. Define the angle between the x-axis and this line to be angle a (note: a must be defined so that it is 0<=a<360, not 0<=a<180). You can draw an additional line from your point to the x-axis being parallel to the y-axis if it helps you.

Assuming you know the geometrical definition of sine and cosine it´s quite easy to see that:
x = r*cos(a)
y = r*sin(a)
(both assuming you were chosing the angle the way I did, if you didn´t y = -r*sin(a) might be your solution).

The other way round is also quite easy to see though a bit harder to write down.

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