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

Algebra ->  Trigonometry-basics -> 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      Log On


   

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(52803) About Me  (Show Source):
You can put this solution on YOUR website!
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Solve sin%282theta%29 + sin%28theta%29%29%29 = 0
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The double-argument formula says that sin%282theta%29 = 2%2Asin%28theta%29%2Acos%28theta%29. 

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


Substitute it into the original equation, and you will get

2%2Asin%28theta%29%2Acos%28theta%29 + sin%28theta%29 = 0.

Now factor it:

sin%28theta%29.%282cos%28theta%29%2B1%29 = 0.

Thus you get two equations:

1) sin%28theta%29 = 0,  which has two solutions  theta = 0 and pi in the given interval for theta.


2) 2cos%28theta%29%2B1 = 0,  or cos%28theta%29 = -1%2F2, which has two solutions theta = 2pi%2F3 and 4pi%2F3.

Answer. The solutions are theta = 0, 2pi%2F3, pi and 4pi%2F3.


Answer by usman_mani(1) About Me  (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.