Find the Exact Value Under the Given Conditions $\sin \alpha = \frac { 7 } { 25 } , 0 < \alpha < \frac { \pi } { 2 } ; \quad \cos \beta = \frac { 20 } { 29 } , 0 < \beta < \frac { \pi } { 2 } \quad$

question 279

Multiple Choice

Find the exact value under the given conditions.
- $\sin \alpha = \frac { 7 } { 25 } , 0 < \alpha < \frac { \pi } { 2 } ; \quad \cos \beta = \frac { 20 } { 29 } , 0 < \beta < \frac { \pi } { 2 } \quad$ Find $\cos ( \alpha + \beta )$ .

• A) \(\frac { 333 } { 725 }\)
• В) \(\frac { 644 } { 725 }\)
• C) \(- \frac { 364 } { 725 }\)
• D) \(\frac { 627 } { 725 }\)

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Definitions:

Diene

Organic compounds containing two double bonds, often involved in polymerization reactions and serving as key intermediates in organic synthesis.

Lowest Occupied

In quantum chemistry, it refers to the lowest energy orbital that contains electrons under normal conditions.

1,3-Butadiene

A colorless, flammable gas with a mild odorous smell, used in the production of synthetic rubber and other polymers.

HOMO

Stands for Highest Occupied Molecular Orbital, the topmost energy level occupied by electrons in a molecule under normal conditions.