9.5 General Equation of a Line

Solved Examples

Move constant to RHS: $\sqrt{3}x + y = 8$ .
Divide by $\sqrt{A^2+B^2} = \sqrt{(\sqrt{3})^2 + 1^2} = \sqrt{4} = 2$ . $\frac{\sqrt{3}}{2}x + \frac{1}{2}y = 4$
Compare with $x \cos \omega + y \sin \omega = p$ . $p = 4$ . $\cos \omega = \sqrt{3}/2, \sin \omega = 1/2$ . Since both are positive, $\omega$ is in 1st quadrant. $\omega = 30^\circ (\pi/6)$ . Normal Form: $x \cos 30^\circ + y \sin 30^\circ = 4$ .

Interactive Solver