Polar Coordinates

Polar to Cartesian

x = r \cos (θ)

y = r \sin (θ)

r^{2} = x^{2} + y^{2}

t a n (θ) = \frac{y}{x}

This consists of $(r, θ, z)$

x = r \cos (θ)

y = r \sin (θ)

z = z

r^{2} = x^{2} + y^{2}

\tan (θ) = \frac{y}{x}

z = z

This consists of $(ρ, θ, ϕ)$

x = ρ \sin (ϕ) \cos (θ)

y = ρ \sin (ϕ) \sin (θ)

z = ρ \cos (ϕ)

ρ = \sqrt{x^{2} + y^{2} + z^{2}}

\tan (θ) = \frac{y}{x}

\cos (ϕ) = \frac{z}{\sqrt{x^{2} + y^{2} + z^{2}}} = \frac{z}{ρ}

r = ρ \sin (θ)

θ = θ

z = ρ \cos (ϕ)

ρ = \sqrt{r^{2} + z^{2}}

θ = θ

\cos (ϕ) = \frac{z}{\sqrt{r^{2} + z^{2}}}