Use the Half-Angle Formulas to Determine the Exact Value of the Given

question 24

Multiple Choice

Use the half-angle formulas to determine the exact value of the given trigonometric expression. $\tan \frac { 3 \pi } { 8 }$

• A) \(\quad \tan \frac { 3 \pi } { 8 } = \sqrt { 2 } - 1\)
• B)\(\tan \frac { 3 \pi } { 8 } = \frac { \sqrt { 2 + \sqrt { 2 } } } { 4 }\)
• C) \(\tan \frac { 3 \pi } { 8 } = \sqrt { 2 } + 1\)
• D)\(\tan \frac { 3 \pi } { 8 } = - \frac { \sqrt { 2 - \sqrt { 2 } } } { 4 }\)
• E) \(\tan \frac { 3 \pi } { 8 } = \sqrt { 2 - \sqrt { 2 } }\)

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Definitions:

Population Variances

A measure of the dispersion of a population's data points from its mean.

Population Proportions

The fraction or percentage of a population that is characterized by a certain trait or attribute.

Sample Proportions

The ratio of members in a subset of a population to the total population, used in statistical analysis.

Normal Distribution

A bell-shaped probability distribution characterized by its mean and standard deviation, describing how data values are spread around the mean.