Find the Exact Value Under the Given Conditions $\cos \alpha = \frac { 1 } { 3 } , 0 < \alpha < \frac { \pi } { 2 } ; \quad \sin \beta = - \frac { 1 } { 2 } , - \frac { \pi } { 2 } < \beta < 0 \quad$

question 53

Multiple Choice

Find the exact value under the given conditions.
- $\cos \alpha = \frac { 1 } { 3 } , 0 < \alpha < \frac { \pi } { 2 } ; \quad \sin \beta = - \frac { 1 } { 2 } , - \frac { \pi } { 2 } < \beta < 0 \quad$ Find $\tan ( \alpha + \beta )$ .

• A) \(\frac { 9 \sqrt { 3 } + 8 \sqrt { 2 } } { 3 }\)
• B) \(\frac { 9 \sqrt { 3 } + 8 \sqrt { 2 } } { 5 }\)
• C) \(\frac { 9 \sqrt { 3 } - 8 \sqrt { 2 } } { 5 }\)
• D) \(\frac { 9 \sqrt { 3 } - 8 \sqrt { 2 } } { 3 }\)

---

Definitions:

Assignment

A transfer of rights, property, or responsibilities from one party to another.

Defenses

Arguments and strategies used in legal proceedings by the defendant to challenge, mitigate, or nullify the claims made by the plaintiff.

Equity Credit

The provision of credit or financing based on the borrower's ownership stakes in assets rather than on their creditworthiness alone.

Negotiable Instrument

A written promise to pay a certain sum of money, which can be demanded or paid at an agreed time, specifying the person responsible for payment in the document.