Find the Exact Value of the Expression $\sin \left( \sin ^ { - 1 } \frac { 2 } { 3 } + \cos ^ { - 1 } \frac { 1 } { 3 } \right)$

question 307

Multiple Choice

Find the exact value of the expression.
- $\sin \left( \sin ^ { - 1 } \frac { 2 } { 3 } + \cos ^ { - 1 } \frac { 1 } { 3 } \right)$

• A) \(\frac { 2 + 2 \sqrt { 10 } } { 9 }\)
• B) \(\frac { 2 \sqrt { 3 } + 2 \sqrt { 10 } } { 9 }\)
• C) \(\frac { 2 \sqrt { 6 } } { 5 }\)
• D) \(\frac { 2 \sqrt { 3 } } { 5 }\)

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Definitions:

Affirmative Proposition

A statement that asserts the truth of something, as opposed to denying it.

Modern View

Contemporary perspective or way of thinking in contrast to traditional views.

Existential Import

The implication or assumption within a statement or proposition that asserts the existence of something.

Lakes

Large bodies of standing freshwater formed in hollows on the earth's surface, often fed by rivers or streams.