Find the Exact Value of the Expression, If Possible $\sin ^ { - 1 } \left[ \sin \left( \frac { 4 \pi } { 7 } \right) \right]$

question 365

Multiple Choice

Find the exact value of the expression, if possible. Do not use a calculator.
- $\sin ^ { - 1 } \left[ \sin \left( \frac { 4 \pi } { 7 } \right) \right]$

• A) \(\frac { 3 \pi } { 7 }\)
• B) \(\frac { 4 \pi } { 7 }\)
• C) \(\frac { 7 } { 4 \pi }\)
• D) \(\frac { 7 } { 3 \pi }\)

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Definitions:

Reciprocity

A social exchange principle where the actions of one party lead to a response by another party, typically in a manner that mirrors the original action.

Norm Of Reciprocity

A social expectation that dictates individuals should return favors and kindnesses that others have provided to them, creating a basis for cooperative behavior.

Social Exchange

A concept proposing that the formation of human connections is guided by an individual assessment of potential gains and losses, alongside an evaluation of other options.

Norms

Social rules that dictate the expected behavior in a particular group or society.