# Thread: Algebraic Solution OF Sine Equations

1. ## Algebraic Solution OF Sine Equations

Solve algebraically the equation
sin2x + sinx = 0 "0<= x <=360"

2. Hello, r_maths!

Solve algebraically: . $\sin2x + \sin x \:= \:0,\quad 0^o \leq x \leq 360^o$

Double-angle Identity: . $\sin2\theta \:=\:2\sin\theta\cos\theta$

Our equation becomes: . $2\sin x\cos x + \sin x \:=\:0$

. . . . . . . . . . . Factor: . . $\sin x(2\cos x + 1)\:=\:0$

And we have two equations to solve:

. . $\sin x\:=\:0\quad\Rightarrow\quad\boxed{x \:=\:0^o,\,180^o,\,360^o}$

. . $2\cos x + 1 \:=\:0\quad\Rightarrow\quad\cos x \:=\:\text{-}\frac{1}{2}\quad\Rightarrow\quad\boxed{x \:=\:120^o,\,240^o}$

3. man, you guys are amazing.