Question

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

Answer 1

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)`.