How do you find the polar coordinates given the rectangular coordinates (1,sqrt3)?

1 Answer
Alex P.
Apr 24, 2017

#(1, sqrt(3))# in rectangular coordinates is #(2, pi/3)# in polar coordinates.

Explanation:

To translate rectangular to polar coordinates we use the follow:
#x=r cos(theta)#
#y=r sin(theta)#

From your question we can set up the equations:
#1=r cos(theta)#
#sqrt(3)=r sin(theta)#

Solve these simultaneous equations by division first:
#sqrt(3)/1 = sin(theta)/cos(theta)#
#sqrt(3) = tan(theta)#
#theta = pi/3#

Now substitute to find #r#:
#1=r cos(pi/3)#
#1=r 1/2#
#2=r#

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