How do you convert (3, - 4) into polar coordinates?

1 Answer
Alan P.
Jan 4, 2016

(r,theta)=(5,2pi+arctan(-3/4)) (approximately =(5,5.64)

Explanation:

The radius r is given by the Pythagorean Theorem as
color(white)("XXX")r=sqrt((-4)^2+3^2) = 5

The value of theta is based on the arctan(y/x) but is dependent upon the quadrant in which (x,y) is positioned. This is because the arctan function returns a value in the range [-pi/2,+pi/2] relative to the X-axis.

{: (color(black)("Quadrant"),,color(white)("XXX")color(black)(theta)), (bar(color(white)("XXXXXX")),,bar(color(white)("XXXXXX"))), (I,,arctan(y/x)), (II,,arctan(y/x)+pi), (III,,arctan(y/x)+pi), (IV,,arctan(y/x)+2pi) :}

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