Find the Exact Value of the Expression, If Possible $\cos ^ { - 1 } \left( \cos \frac { 7 \pi } { 6 } \right)$

question 252

Multiple Choice

Find the exact value of the expression, if possible. Do not use a calculator.
- $\cos ^ { - 1 } \left( \cos \frac { 7 \pi } { 6 } \right)$

• A) \(\frac { 5 \pi } { 6 }\)
• B) \(\frac { 4 \pi } { 3 }\)
• C) \(\frac { \pi } { 6 }\)
• D) \(\frac { \pi } { 3 }\)

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Definitions:

Cyclohexane Derivative

A chemical compound derived from cyclohexane by replacing one or more of its hydrogen atoms with other atoms or groups.

Alkyl Substituents

Alkyl substituents are groups of atoms, derived from alkanes, that are attached to a molecule, replacing a hydrogen atom.

Equatorial

Refers to the position around a cyclic molecule where substituents are located in the plane or nearly in the plane of the ring, reducing steric hindrance.

Energy Conformation

The spatial arrangement of atoms in a molecule that relates to its energy level, often describing structures that are energetically favorable or unfavorable.