How do you convert the Cartesian coordinates (1.1 m, 1.6 m) to polar coordinates?

1 Answer
David G.
Feb 14, 2016

Rectangular (Cartesian) coordinates are in the form #(x,y)#, polar coordinates in the form #(r,theta)#. In this case the polar coordinates are #(1.45,0.97)#.

Explanation:

First step is to find #r#, the distance of the point from the origin:

#r=sqrt(x^2+y^2)=sqrt(1.1^2+1.6^2)=sqrt3.77=1.94# #m#.

Now we need to find the angle, #theta#, in radians, counterclockwise from the positive #x# axis. To do this we use trigonometry: the #x# and #y# coordinates are the adjacent and opposite sides respectively of a right-angled triangle.

#tan theta=(opp)/(adj)=1.6/1.1=1.45#

#theta=tan^-1(1.45)=0.97# radians

Putting it together, the polar coordinates of the point are #(1.45,0.97)#.

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