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

1 Answer
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).