SOLUTION: Use a Double- or Half-Angle Formula to solve the equation in the interval [0, 2π). (Enter your answers as a comma-separated list.) sin(2θ) + sin(θ) = 0

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Question 1009491: Use a Double- or Half-Angle Formula to solve the equation in the interval [0, 2π). (Enter your answers as a comma-separated list.)
sin(2θ) + sin(θ) = 0
Found 2 solutions by ikleyn, usman_mani:
Answer by ikleyn(52804)   (Show Source): You can put this solution on YOUR website!
.
Solve + =
------------------------------------------------------- 
The double-argument formula says that  = . 

(See, for example, the lesson Trigonometric functions of multiply argument in this site).


Substitute it into the original equation, and you will get

 +  = .

Now factor it:

. = .

Thus you get two equations:

1)  = ,  which has two solutions   =  and  in the given interval for .


2)  = ,  or  = , which has two solutions  =  and .

Answer. The solutions are  = , ,  and .


Answer by usman_mani(1)   (Show Source): You can put this solution on YOUR website!
sin(2θ) + sinθ = 0
2sinθcosθ + sinθ = 0
2sinθcosθ = -sinθ
sinθ = 0, cosθ = -½
θ = 0, π, 2π/3, 4π/3
I think its correct.
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