Solve θ=6/11+f(sin140^circ)

$$\theta = 6 / 11 + f ( \sin 140 ^ { \circ } )$$

Solve for f_0

$$f_{0}=\frac{2000000000000000\theta }{1285575219373079}-\frac{12000000000000000}{14141327413103869}$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$\theta = \frac{6}{11} + f 0.6427876096865395$$

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

$$\frac{6}{11}+f_{0}\times 0.6427876096865395=\theta$$

Subtract \frac{6}{11} from both sides.

$$f_{0}\times 0.6427876096865395=\theta -\frac{6}{11}$$

The equation is in standard form.

$$0.6427876096865395f_{0}=\theta -\frac{6}{11}$$

Divide both sides of the equation by 0.6427876096865395, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{0.6427876096865395f_{0}}{0.6427876096865395}=\frac{\theta -\frac{6}{11}}{0.6427876096865395}$$

Dividing by 0.6427876096865395 undoes the multiplication by 0.6427876096865395.

$$f_{0}=\frac{\theta -\frac{6}{11}}{0.6427876096865395}$$

Divide \theta -\frac{6}{11} by 0.6427876096865395 by multiplying \theta -\frac{6}{11} by the reciprocal of 0.6427876096865395.

$$f_{0}=\frac{2000000000000000\theta }{1285575219373079}-\frac{12000000000000000}{14141327413103869}$$

Solve for θ

$$\theta =\frac{1285575219373079f_{0}}{2000000000000000}+\frac{6}{11}$$