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Solve on the interval [0,21): 2-3 1 - cos 9 = 2 O A. O B. *** 3 Oc. 7 117 6 7 T 11T O D.

Solve on the interval [0,21): 2-3 1 - cos 9 = 2 O A. O B. *** 3 Oc. 7 117 6 7 T 11T-example-1

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Subtracting 1 to the given equation we get:


\begin{gathered} 1-\cos \theta-1=\frac{2-\sqrt[]{3}}{2}-1, \\ -\text{cos}\theta=-\frac{\sqrt[]{3}}{2}\text{.} \end{gathered}

Multiplying by -1 we get:


\begin{gathered} -\cos \theta\cdot(-1)=-\frac{\sqrt[]{3}}{2}\cdot(-1), \\ \cos \theta=\frac{\sqrt[]{3}}{2}\text{.} \end{gathered}

Now, notice that:


\begin{gathered} \cos ((\pi)/(6)+2n\pi)=\frac{\sqrt[]{3}}{2}, \\ \cos ((11\pi)/(6)+2n\pi)=\frac{\sqrt[]{3}}{2}\text{.} \end{gathered}

Therefore the solutions of the given equation in the interval [0,2π] are:


(\pi)/(6),(11\pi)/(6).

Answer: Option C.

User Realtek
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