Solve P=UIcos(varphi)

$$P = U I \cos ( \varphi )$$

Solve for I

$$\left\{\begin{matrix}I=\frac{P}{U\cos(\phi )}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }\phi =\pi n_{1}+\frac{\pi }{2}\text{ and }U\neq 0\\I\in \mathrm{R}\text{, }&\left(U=0\text{ or }\exists n_{1}\in \mathrm{Z}\text{ : }\phi =\pi n_{1}+\frac{\pi }{2}\right)\text{ and }P=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$UI\cos(\phi )=P$$

The equation is in standard form.

$$U\cos(\phi )I=P$$

Divide both sides by U\cos(\phi ).

$$\frac{U\cos(\phi )I}{U\cos(\phi )}=\frac{P}{U\cos(\phi )}$$

Dividing by U\cos(\phi ) undoes the multiplication by U\cos(\phi ).

$$I=\frac{P}{U\cos(\phi )}$$

Solve for P

$$P=IU\cos(\phi )$$