kjuchiha 2 years ago Please help: Find all solutions to the equation. sin^2(x) + sin (x) = 0

1. mukushla

ok u know that$\sin 2x=2 \sin x\cos x$so equation becomes$2 \sin x\cos x+\sin x=0$take out common factor$\sin x(2\cos x+1)=0$using zero product property$\sin x=0$or$2\cos x+1=0$

2. kjuchiha

but the equation is sin^2(x)

3. mukushla

oh sorry$\sin^2 x+\sin x=0$take out common factor$\sin x(\sin x+1)=0$easier :)

4. mukushla

$\sin x=0$or$\sin x=-1$

5. mukushla

makes sense?

6. kjuchiha

a little but i dont know how to get the solutions

7. Supenova

u start like this: Let x be sin(x) and x^2+x=0 x(x+1)=0 then, x=0; & x=-1 sin is at radian -3/4pi and pi

8. Supenova

u substitute x value in sin(x) and -1 is co-terminal (270) angle and 0