Question

If $(x,y)$ represents the Cartesian coordinates for the polar coordinates $(4,\theta )$, then the correct relationship between $x$ and $y$ is

• A. $x^2+y^2=4$
• B. $x^2+y^2=16$
• C. $x^2+y^2=2$
• D. $x^2+y^2=64$

Answer 1

The correct option is B $x^2+y^2=16$

We know the conversion formula of Cartesian to polar is
$x=4\cos \theta ,y=4\sin \theta$
Now, we know that
${\sin }^2\theta +{\cos }^2\theta =1\Rightarrow x^2+y^2=16$