Find the Exact Value of the Expression $$\sin ^ { - 1 } \left[ \sin \left( \frac { \pi } { 5 } \right) \right]$$

question 14

Multiple Choice

Find the exact value of the expression. Do not use a calculator.
- $$\sin ^ { - 1 } \left[ \sin \left( \frac { \pi } { 5 } \right) \right]$$

• A) \(5 \pi\)
• B) \(\frac { \pi } { 5 }\)
• C) \(- 5 \pi\)
• D) \(- \frac { \pi } { 5 }\)

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Definitions:

Self-awareness

The conscious knowledge of one's own character, feelings, motives, and desires, which can play a key role in personal development.

Self-conceptualization

The process by which an individual forms, defines, and perceives their own identity and characteristics.

Self-recognition

The ability of an individual to recognize themselves as a separate entity, often tested through the mirror test in humans and animals.

Self-evaluation

The process through which an individual assesses their own abilities, achievements, and behaviors in relation to personal standards or societal norms.