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:

Activity Variance

The difference between the budgeted amount of activity and the actual amount of activity, which can impact costs and operational efficiency.

Cost Formula

An equation used to predict costs at various levels of activity, incorporating both fixed and variable cost components.

Travel Expenses

Costs associated with traveling for business purposes, such as transportation, lodging, and meals.

Variable Cost

A cost that varies with the level of output or production, such as materials or labor costs.