Find the Exact Value Under the Given Conditions Find $\cos ( \alpha + \beta )$

question 48

Multiple Choice

Find the exact value under the given conditions.
- $\cos \alpha = - \frac { 4 } { 5 } , \frac { \pi } { 2 } < \alpha < \pi ; \quad \sin \beta = - \frac { \sqrt { 21 } } { 5 } , \pi < \beta < \frac { 3 \pi } { 2 } \quad$ Find $\cos ( \alpha + \beta )$ .

• A) \(\frac { - 6 + 4 \sqrt { 21 } } { 25 }\)
• B) \(\frac { 8 + 3 \sqrt { 21 } } { 25 }\)
• C) \(\frac { 6 - 4 \sqrt { 21 } } { 25 }\)
• D) \(\frac { - 8 - 3 \sqrt { 21 } } { 25 }\)

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Definitions:

Statistic

A numerical value that summarizes or describes an aspect of a sample.

Parameter

A measurable characteristic that describes an aspect of a population in statistical analysis.

Standard Deviation

A statistical analysis tool that calculates the spread of a dataset relative to its mean.