Answer to Question #212834 in Physics for mikay

Question

the cartesian coordinates of a point are given by (x,y)=(-2.5,-3.5) meters. Find the polar coordinates of this point?

Answer 1

The polar coordinates are related with cartesian coordinates by next equations

$$\rho=\sqrt{x^2+y^2}, \quad \theta=\tan^{-1}\frac{y}{x}$$

We get

$$\rho=\sqrt{(-2.5)^2+(-3.5)^2}=4.3, \\ \theta=\tan^{-1}\frac{-3.5}{-2.5}=234^{\circ}$$