Solve the Multiple-Angle Equation $\sin \frac { 3 x } { 6 } = - \frac { \sqrt { 3 } } { 2 }$

question 14

Multiple Choice

Solve the multiple-angle equation.​ $\sin \frac { 3 x } { 6 } = - \frac { \sqrt { 3 } } { 2 }$ ​

• A) \(\frac { \pi } { 3 } + 3 n \pi , \frac { 2 \pi } { 3 } + 3 n \pi\)
• B)​ \(\frac { \pi } { 3 } + 2 n \pi , \frac { 2 \pi } { 3 } + 2 n \pi\)
• C)​ \(\frac { 8 \pi } { 3 } + 4 n \pi , \frac { 10 \pi } { 3 } + 4 n \pi\)
• D)​ \(\frac { 5 \pi } { 3 } + 2 n \pi , \frac { 4 \pi } { 3 } + 3 n \pi\)
• E)​ \(\frac { \pi } { 3 } + 4 n \pi , \frac { 2 \pi } { 3 } + 4 n \pi\)

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Definitions:

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Rapid evolutionary diversification within a lineage, resulting in the formation of many new species.

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Warm-blooded, feathered vertebrates that lay eggs, characterized by their ability to fly, although some species are flightless.

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The process by which organisms adjust to changes in their environment, often leading to evolutionary changes that improve survival and reproduction.

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A form of oxygen with three atoms per molecule, forming a layer in the Earth's atmosphere that absorbs most of the sun's ultraviolet radiation.