Find the Exact Value of the Expression, If Possible $\sin \left( \tan ^ { - 1 } x \right)$

question 328

Multiple Choice

Find the exact value of the expression, if possible. Do not use a calculator.
- $\sin \left( \tan ^ { - 1 } x \right)$

• A) \(\frac { x \sqrt { x ^ { 2 } + 1 } } { x ^ { 2 } + 1 }\)
• B) \(\frac { x \sqrt { x ^ { 2 } - 1 } } { x ^ { 2 } - 1 }\)
• C) \(x \sqrt { x ^ { 2 } + 1 }\)
• D) \(\frac { \sqrt { x ^ { 2 } + 1 } } { x ^ { 2 } + 1 }\)

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Definitions:

Long-Term Memory Storage

The process of retaining information over extended periods, ranging from days to a lifetime.

Frontal Lobes

The part of the brain located at the front of each cerebral hemisphere, responsible for voluntary movement, expressive language, and managing higher level executive functions.

Three-Stage Model

A model that describes memory processing in three distinct stages: sensory memory, short-term (or working) memory, and long-term memory.

Memory Storage

The process by which information is encoded, stored, and retrieved in the brain, forming the basis for learning and remembering.