Solve a_{x}*a_{rho}=cosphi

$$a _ { x } \cdot a _ { \rho } = \cos \phi$$

Solve for a_x

$$\left\{\begin{matrix}a_{x}=\frac{\cos(ϕ)}{a_{ρ}}\text{, }&a_{ρ}\neq 0\\a_{x}\in \mathrm{R}\text{, }&\exists n_{1}\in \mathrm{Z}\text{ : }ϕ=\pi n_{1}+\frac{\pi }{2}\text{ and }a_{ρ}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$a_{ρ}a_{x}=\cos(ϕ)$$

Divide both sides by a_{ρ}.

$$\frac{a_{ρ}a_{x}}{a_{ρ}}=\frac{\cos(ϕ)}{a_{ρ}}$$

Dividing by a_{ρ} undoes the multiplication by a_{ρ}.

$$a_{x}=\frac{\cos(ϕ)}{a_{ρ}}$$

Solve for a_ρ

$$\left\{\begin{matrix}a_{ρ}=\frac{\cos(ϕ)}{a_{x}}\text{, }&a_{x}\neq 0\\a_{ρ}\in \mathrm{R}\text{, }&\exists n_{1}\in \mathrm{Z}\text{ : }ϕ=\pi n_{1}+\frac{\pi }{2}\text{ and }a_{x}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$a_{x}a_{ρ}=\cos(ϕ)$$

Divide both sides by a_{x}.

$$\frac{a_{x}a_{ρ}}{a_{x}}=\frac{\cos(ϕ)}{a_{x}}$$

Dividing by a_{x} undoes the multiplication by a_{x}.

$$a_{ρ}=\frac{\cos(ϕ)}{a_{x}}$$