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.
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