Question

How do I convert Cartesian coordinates to polar coordinates?

Answer 1

The Cartesian coordinates of a point are (x, y).
'x' and 'y'are both distances.

The polar coordinates of the same point are (R, A).
'R' is a distance. 'A' is an angle.

How to find 'R' and 'A' when you know 'x' and 'y' :

R = distance of the point from the origin = square root of (x² + y²)

A = angle clockwise from the x-axis to the point = angle whose tangent is (y/x)

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If you HAVE the polar coordinates and you want to find the Cartesian ones,
then do it like this:

You have (R, A) .

You want to find 'x' and 'y' .

x = R cos(A)

y = R sin(A)

Answer 2

`Solving\ right\ triangle\ with\ two\ known\ sides. \ Cartesian\ coordinates\\ tell \ us\ about\ those\ sides.\ Example:\\ Coordinates\ (a,b)\ sides:\ a\ and\ b. \\ \\\\ From\ Pythagorean\ theorem\ find\ third\ side:\\ r^2=a^2+b^2\\ r=√(a^2+b^2)\\\\Using\ tangent\ function\ find\ angle:\\tan( \alpha )=(b)/(a)\\ \alpha =tan^(-1)\\\\Polar\ coordinates: \ (r, \alpha )`