Question 6556
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 = {{{sqrt(x^2 + y^2)}}} --> Pythagoras.

--> this gives angle A = 56.3degrees and r = {{{sqrt(13)}}}


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 {{{sqrt(13)}}}


Is this OK for you?


jon.