Solve f(x)=sin(pi/2+varphi)

$$f ( x ) = \sin ( \frac { \pi } { 2 } + \varphi )$$

Solve for f

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

Steps for Solving Linear Equation

The equation is in standard form.

$$xf=\sin(\phi +\frac{\pi }{2})$$

Divide both sides by x.

$$\frac{xf}{x}=\frac{\sin(\frac{2\phi +\pi }{2})}{x}$$

Dividing by x undoes the multiplication by x.

$$f=\frac{\sin(\frac{2\phi +\pi }{2})}{x}$$

Solve for x

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

Steps for Solving Linear Equation

The equation is in standard form.

$$fx=\sin(\phi +\frac{\pi }{2})$$

Divide both sides by f.

$$\frac{fx}{f}=\frac{\sin(\frac{2\phi +\pi }{2})}{f}$$

Dividing by f undoes the multiplication by f.

$$x=\frac{\sin(\frac{2\phi +\pi }{2})}{f}$$