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

question 8

Multiple Choice

Find the exact value under the given conditions.
- $\cos \alpha = - \frac { 24 } { 25 } , \frac { \pi } { 2 } < \alpha < \pi ; \quad \sin \beta = - \frac { \sqrt { 21 } } { 5 } , \pi < \beta < \frac { 3 \pi } { 2 } \quad$ Find $\tan ( \alpha + \beta )$

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

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Definitions:

Utility-Maximizing

A principle in economics where consumers allocate their income to purchase goods and services that provide the highest satisfaction or utility.

Staples

Basic or essential food items and products that are consumed regularly and necessary for daily living.

Paper Clips

Small pieces of bent wire or plastic used for holding sheets of paper together.

Utility-Maximizing

The process by which individuals choose consumption bundles that will give them the greatest amount of satisfaction or utility.