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

question 7

Multiple Choice

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

• A)​​ \(x = \frac { 2 \pi } { 3 } + 2 n \pi \text { and } x = \frac { 5 \pi } { 3 } + 2 n \pi\) ,where n is an integer
• B)​ \(x = \frac { 7 \pi } { 6 } + 2 n \pi \text { and } x = \frac { 11 \pi } { 6 } + 2 n \pi\) ,where n is an integer
• C)​ \(x = \frac { \pi } { 2 } + n \pi\) ,where n is an integer
• D) \(x = \frac { \pi } { 2 } + 2 n \pi \text { and } x = \frac { 3 \pi } { 2 } + 2 n \pi\) ,where n is an integer
• E) \(x = \frac { \pi } { 2 } + 4 n \pi \text { and } x = \frac { 3 \pi } { 2 } + 4 n \pi\) ,where n is an integer

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Definitions:

War And Terrorism

Acts of violence and conflict intended to achieve political, religious, or ideological objectives, often at the expense of civilian peace and security.

Resiliency

The ability of a person to adapt well and recover quickly from stress, adversity, or tragedy.

Storytelling

The act of narrating stories, an ancient and universal human activity used for entertainment, education, and cultural preservation.

Inappropriate Touches

Physical interactions that violate personal boundaries, often without consent or in contexts where consent cannot be freely given.