Question

Express the Cartesian coordinates (-4, 0) as polar coordinates.(4, 2π)(4, 3π/2)(4, π/2)(4, π)

Answer 1

Polar coordinates are expressed as (r, θ), where:

$\begin{gathered} r=\sqrt[]{x^2+y^2} \\ \theta=\arctan (\frac{y}{x}) \end{gathered}$

Substituting with the point (-4, 0), we get:

$\begin{gathered} r=\sqrt[]{x^2+y^2} \\ r=\sqrt[]{(-4)^2+0^2} \\ r=\sqrt[]{16} \\ r=4 \end{gathered}$$\begin{gathered} \theta=\arctan (\frac{0}{-4}) \\ \theta=\arctan (0) \\ \theta=\pi \end{gathered}$

The point is (4, π)