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

question 100

Multiple Choice

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

• A) \(x = \frac { 5 \pi } { 3 } + n \pi\)
• B) \(x = \frac { 7 \pi } { 6 } + n \pi \text { and } \frac { 11 \pi } { 6 } + n \pi\)
• C) \(x = \frac { 2 \pi } { 3 } + n \pi\)
• D) \(x = \frac { 5 \pi } { 6 } + n \pi \text { and } \frac { 7 \pi } { 6 } + n \pi\)
• E) \(x = \frac { \pi } { 3 } + 2 n \pi\)

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Definitions:

Sample Means

The average value of a sample, which is a subset of a larger population, used to estimate the population mean.

Normally Distributed

A statistical distribution where data points are symmetrically distributed around the mean, forming a bell-shaped curve.

Standard Deviation

An indicator of the degree to which a dataset's values vary or are spread, showing the distance of the values from the average.

Probability

The measure or quantification of how likely an event is to occur, expressed as a number between 0 (impossible) and 1 (certain).