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

question 203

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) \(\frac { 2 \sqrt { 3 } } { 5 }\)

---

Definitions:

Psychoanalytic Methods

Techniques used in psychoanalysis to explore the unconscious mind, including free association, dream interpretation, and analysis of transference.

Objective Reality

The state of things as they actually exist, independently of human consciousness or perceptions.

Dynamic Traits

Personality characteristics that are active and influential in an individual's thought patterns, behaviors, and emotional responses.

Temperament Traits

Inborn personality characteristics that influence how individuals react to the environment emotionally and behaviorally from an early age.