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:

Mutually Exclusive

Events or conditions that cannot occur simultaneously or cannot both be true at the same time.

Addition Rule

A principle in probability theory that determines the probability of the occurrence of at least one of two events, taking into account their joint probability if they are not mutually exclusive.

Probability

A numerical quantification of the likelihood that a particular event will occur, often expressed as a number between 0 and 1, where 1 indicates certainty.

Rolling a Pair

The act of throwing two dice simultaneously and observing the outcome, often used in probability calculations.