# SOLUTION: Dear Sir/Madam, I am confronted with the following problem: "Give polar coordinates of a point whose rectangular coordinates are (-2,3)." I have never previously dealt with

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 Question 6556: Dear Sir/Madam, I am confronted with the following problem: "Give polar coordinates of a point whose rectangular coordinates are (-2,3)." I have never previously dealt with polar coordinates. I looked it up and am entirely confused. Could you help me in solving this question? Thanks in advance. Regards, -Mike Answer by longjonsilver(2297)   (Show Source): You can put this solution on YOUR website!Mike, where is your teacher? Right then, polar and Cartesian coordinates. Imagine a set of axes and the point (2,3). This lies in the first quadrant. The +ve x-axis is the zero line, then the +y axis is the 90 degree line. The -ve x-axis is the 180 degree line etc., circling round back to the +ve x-axis at 360 degrees. Right...plot the point P(2,3). Create a right angled triangle OPX, where O is the origin, X is the vertical line from point P to the x-axis. OK, so far? We can describe the point P in 2 ways: 1. Cartesian Coordinates - reference the x and y values --> (2,3) 2. Polar Coordinates - reference the angle, A, from the zero line (the +ve x-axis) and the length, r, to the point from the origin. This length is the length of OP, the hypotenuse of the triangle. So, tanA = y/x and r = --> Pythagoras. --> this gives angle A = 56.3degrees and r = Now, your point is actually (-2, 3), so this lies in Quadrant 2. If you draw your triangle there again, you find another angle, call it B, also 56.3. However, strictly, this is 180-56.3 = 123.7 degrees. Check it..tan(123.7) is -1.5: correct! and r is still Is this OK for you? jon.