Find the Exact Solutions of the Given Equation in the Interval

question 1

Multiple Choice

Find the exact solutions of the given equation in the interval $[ 0,2 \pi )$ .
$$2 \sin ^ { 2 } x + \sin x = 1$$

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

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Definitions:

Extreme Values

The smallest or largest values in a data set or distribution, often considered as outliers or as significant for their rarity.

Variation

Variation refers to the extent to which data points in a data set differ from each other and from the mean of the dataset.

Standard Deviation

A measure that quantifies the amount of variation or dispersion of a set of data values from the mean value.

Standard Deviation

A quantification of the range or diversity in a dataset, illustrating the difference of the numbers from their mean value.