Write an Algebraic Expression That Is Equivalent To $\sin \left( \arctan \frac { x } { 2 } \right)$

question 259

Multiple Choice

Write an algebraic expression that is equivalent to $\sin \left( \arctan \frac { x } { 2 } \right)$ .

• A) \(\frac { x \sqrt { x ^ { 2 } + 4 } } { x ^ { 2 } + 4 }\)
• B) \(\frac { 2 \sqrt { x ^ { 2 } + 4 } } { x ^ { 2 } + 4 }\)
• C) \(\frac { 2 } { x }\)
• D) \(\frac { \sqrt { x ^ { 2 } + 4 } } { 2 }\)
• E) \(\frac { \sqrt { x ^ { 2 } + 4 } } { x }\)

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Definitions:

Reality Principle

A concept in psychoanalysis that describes the ability of the mind to assess the external world and act upon it accordingly, as opposed to acting on the pleasure principle.

Ego

In psychoanalytic theory, the part of the personality that mediates between the demands of the id, superego, and reality.

Guilt/Pride Principle

A psychological concept that suggests emotions like guilt and pride are fundamental in guiding moral behaviors and forming a sense of personal responsibility.

Id

In psychoanalytic theory, the part of the personality containing innate biological drives and instincts. It operates on the pleasure principle, seeking immediate gratification.