What are the polar coordinates of #(3, 4)#?

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Answer 1 · 2014-09-13T04:15:46

When converting from rectangular coordinates to polar coordinates you use the following 2 formulas.

#x^2+y^2=r^2# AND #theta=tan^-1(y/x)#

Using the values for the ordered pair you make the necessary substitutions for #x and y#.

#3^2+4^2=r^2#
#9+16=r^2#
#25=r^2#
#sqrt(25)=sqrt(r^2)#
#+-5=r#

#theta=tan^-1(y/x)=tan^-1(4/3)=53.13^o#

Solution:

Polar coordinates are in the form #(r,theta) ->(+-5,53.13^o)#

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