Solve tanalpha=-3/12quadtext{Ry}quadsinalpha=

$$\tan \alpha = - \frac { 3 } { 12 } \quad \text { Ry } \quad \sin \alpha =$$

Solve for R

$$\left\{\begin{matrix}R=-\frac{4}{y\cos(\alpha )}\text{, }&y\neq 0\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }\alpha =\pi n_{1}+\frac{\pi }{2}\\R\in \mathrm{R}\text{, }&\exists n_{2}\in \mathrm{Z}\text{ : }\alpha =\pi n_{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Reduce the fraction \frac{3}{12} to lowest terms by extracting and canceling out 3.

$$\tan(\alpha )=-\frac{1}{4}Ry\sin(\alpha )$$

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

$$-\frac{1}{4}Ry\sin(\alpha )=\tan(\alpha )$$

The equation is in standard form.

$$\left(-\frac{y\sin(\alpha )}{4}\right)R=\tan(\alpha )$$

Divide both sides by -\frac{1}{4}y\sin(\alpha ).

$$\frac{\left(-\frac{y\sin(\alpha )}{4}\right)R}{-\frac{y\sin(\alpha )}{4}}=\frac{\tan(\alpha )}{-\frac{y\sin(\alpha )}{4}}$$

Dividing by -\frac{1}{4}y\sin(\alpha ) undoes the multiplication by -\frac{1}{4}y\sin(\alpha ).

$$R=\frac{\tan(\alpha )}{-\frac{y\sin(\alpha )}{4}}$$

Divide \tan(\alpha ) by -\frac{1}{4}y\sin(\alpha ).

$$R=-\frac{4}{y\cos(\alpha )}$$

Solve for y

$$\left\{\begin{matrix}y=-\frac{4}{R\cos(\alpha )}\text{, }&R\neq 0\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }\alpha =\pi n_{1}+\frac{\pi }{2}\\y\in \mathrm{R}\text{, }&\exists n_{2}\in \mathrm{Z}\text{ : }\alpha =\pi n_{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Reduce the fraction \frac{3}{12} to lowest terms by extracting and canceling out 3.

$$\tan(\alpha )=-\frac{1}{4}Ry\sin(\alpha )$$

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

$$-\frac{1}{4}Ry\sin(\alpha )=\tan(\alpha )$$

The equation is in standard form.

$$\left(-\frac{R\sin(\alpha )}{4}\right)y=\tan(\alpha )$$

Divide both sides by -\frac{1}{4}R\sin(\alpha ).

$$\frac{\left(-\frac{R\sin(\alpha )}{4}\right)y}{-\frac{R\sin(\alpha )}{4}}=\frac{\tan(\alpha )}{-\frac{R\sin(\alpha )}{4}}$$

Dividing by -\frac{1}{4}R\sin(\alpha ) undoes the multiplication by -\frac{1}{4}R\sin(\alpha ).

$$y=\frac{\tan(\alpha )}{-\frac{R\sin(\alpha )}{4}}$$

Divide \tan(\alpha ) by -\frac{1}{4}R\sin(\alpha ).

$$y=-\frac{4}{R\cos(\alpha )}$$