Find the Exact Solutions of the Given Equation in the Interval

question 54

Multiple Choice

Find the exact solutions of the given equation in the interval $[ 0,2 \pi )$ . $\sin 2 x = \sin x$

• A) \(x = \frac { 2 \pi } { 3 } , \pi , \frac { 4 \pi } { 3 }\)
• B) \(x = 0 , \frac { \pi } { 3 } , \pi , \frac { 5 \pi } { 3 }\)
• C) \(x = \frac { \pi } { 2 } , \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }\)
• D) \(x = 0 , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 } , \pi , \frac { 4 \pi } { 3 } , \frac { 5 \pi } { 3 }\)
• E) \(x = 0\)

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Definitions:

Lateralization

The tendency for certain functions or processes to be more dominant in one hemisphere of the brain than the other.

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The process by which thoughts are translated into speech, involving several areas of the brain to produce and articulate words.

Broca's Area

A region in the frontal lobe of the dominant hemisphere of the brain associated with language processing, speech production, and comprehension.

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The action of muscles contracting and relaxing, which results in movement of body parts or the entire body.