Solve sin(x)=sum(4+pi)

$$\sin ( x ) = \sum ( 4 + \pi )$$

Solve for Σ

$$Σ=\frac{\sin(x)}{\pi +4}$$

Steps for Solving Linear Equation

Use the distributive property to multiply Σ by 4+\pi .

$$\sin(x)=4Σ+Σ\pi$$

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

$$4Σ+Σ\pi =\sin(x)$$

Combine all terms containing Σ.

$$\left(4+\pi \right)Σ=\sin(x)$$

The equation is in standard form.

$$\left(\pi +4\right)Σ=\sin(x)$$

Divide both sides by 4+\pi .

$$\frac{\left(\pi +4\right)Σ}{\pi +4}=\frac{\sin(x)}{\pi +4}$$

Dividing by 4+\pi undoes the multiplication by 4+\pi .

$$Σ=\frac{\sin(x)}{\pi +4}$$

Solve for x

$$x=-\arcsin(\left(\pi +4\right)Σ)+2\pi n_{1}+\pi \text{, }n_{1}\in \mathrm{Z}$$

$$x=\arcsin(\left(\pi +4\right)Σ)+2\pi n_{2}\text{, }n_{2}\in \mathrm{Z}\text{, }|Σ|\leq \frac{1}{\pi +4}$$