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

1 Answer
Jan 4, 2016

Answer:

#(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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