Decimal to Polar CoordinatesDate: 11/23/97 at 02:03:53 From: Michael Louis Subject: Conversion from decimal to polar coordinates The textbook I'm using for a PreCalculus course in night school shows me how to convert polar coordinates into rectangular ones using the formula: x = r cos theta and y = r sin theta I need to know how to convert in the opposite direction, from rectangular coordinates back to polar. Thank you. Date: 11/23/97 at 05:09:48 From: Doctor Mitteldorf Subject: Re: Conversion from decimal to polar coordinates Dear Michael, If you sum the squares of x and y, you find that you get r squared, since sin^2 + cos^2 = 1 for any angle. Therefore r = sqrt(x^2+y^2) To find theta, divide your two equations y/x = sin(theta)/cos(theta) = tan(theta) You can find theta from the inverse tangent function. You will need to resolve the ambiguity about whether you have theta or (pi+theta) by using the signs of x and y. For example, (x = 1, y = 1) means theta = pi/4, but (x = -1, y = -1) means theta = 3pi/4, even though the tangents of these two angles are the same. -Doctor Mitteldorf, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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