`2sin(x/2) + sqrt(3) = 0` Solve the multiple-angle equation.

Textbook Question

Chapter 5, 5.3 - Problem 44 - Precalculus (3rd Edition, Ron Larson).
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Borys Shumyatskiy | College Teacher | (Level 3) Associate Educator

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`sin(x/2)=-sqrt(3)/2.`

The general solution is

`x/2=(-1)^k*arcsin(-sqrt(3)/2)+kpi, kinZZ.`

So `x=(-1)^(k+1)*(2pi/3)+2kpi, kinZZ,`

because `arcsin(-sqrt(3)/2)=-pi/3.`

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