Atrisiniet fcosθ+sqrt{3}sinθ=2r

$$f \cos \theta + \sqrt { 3 } \sin \theta = 2 r$$

Atrast f (complex solution)

$$\left\{\begin{matrix}f=-\frac{\sqrt{3}\sin(\theta )-2r}{\cos(\theta )}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =\pi n_{1}+\frac{\pi }{2}\\f\in \mathrm{C}\text{, }&r=\frac{\sqrt{3}\sin(\theta )}{2}\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }\theta =\frac{\pi \left(2n_{1}+1\right)}{2}\end{matrix}\right,$$

Lineāra vienādojuma risināšanas darbības

Atņemiet \sqrt{3}\sin(\theta ) no abām pusēm.

$$f\cos(\theta )=2r-\sqrt{3}\sin(\theta )$$

Vienādojums ir standarta formā.

$$\cos(\theta )f=-\sqrt{3}\sin(\theta )+2r$$

Daliet abas puses ar \cos(\theta ).

$$\frac{\cos(\theta )f}{\cos(\theta )}=\frac{-\sqrt{3}\sin(\theta )+2r}{\cos(\theta )}$$

Dalīšana ar \cos(\theta ) atsauc reizināšanu ar \cos(\theta ).

$$f=\frac{-\sqrt{3}\sin(\theta )+2r}{\cos(\theta )}$$

Atrast r

$$r=\frac{f\cos(\theta )+\sqrt{3}\sin(\theta )}{2}$$

Lineāra vienādojuma risināšanas darbības

Mainiet puses tā, lai visi mainīgie locekļi atrastos pa kreisi.

$$2r=f\cos(\theta )+\sqrt{3}\sin(\theta )$$

Daliet abas puses ar 2.

$$\frac{2r}{2}=\frac{f\cos(\theta )+\sqrt{3}\sin(\theta )}{2}$$

Dalīšana ar 2 atsauc reizināšanu ar 2.

$$r=\frac{f\cos(\theta )+\sqrt{3}\sin(\theta )}{2}$$