Use the Given Information to Find the Exact Value of the Expression

question 133

Multiple Choice

Use the given information to find the exact value of the expression.
- $\sin \alpha = - \frac { 24 } { 25 } , \alpha$ lies in quadrant IV, and $\cos \beta = - \frac { \sqrt { 21 } } { 5 } , \beta$ lies in quadrant III Find $\sin ( \alpha - \beta )$ .

• A) \(\frac { 14 + 24 \sqrt { 21 } } { 125 }\)
• B) \(\frac { - 14 + 24 \sqrt { 21 } } { 125 }\)
• C) \(\frac { - 48 + 7 \sqrt { 21 } } { 125 }\)
• D) \(\frac { - 48 - 7 \sqrt { 21 } } { 125 }\)

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Definitions:

T Distribution

A probability distribution that is used to estimate population parameters when the sample size is small and the population variance is unknown.

Population Mean

The average of a set of values in the entire population.

Sample Standard Deviation

A measure of the amount of variation or dispersion of a set of values from a sample, indicating how spread out the values are from the mean of the sample.

Z Value

A Z value is a statistical measure representing the number of standard deviations a data point is from the mean.