Find the Exact Value of the Expression, If Possible $\tan ^ { - 1 } \left[ \tan \left( \frac { 3 \pi } { 5 } \right) \right]$

question 305

Multiple Choice

Find the exact value of the expression, if possible. Do not use a calculator.
- $\tan ^ { - 1 } \left[ \tan \left( \frac { 3 \pi } { 5 } \right) \right]$

• A) \(- \frac { 2 \pi } { 5 }\)
• B) \(\frac { 3 \pi } { 5 }\)
• C) \(- \frac { 3 \pi } { 5 }\)
• D) \(\frac { 2 \pi } { 5 }\)

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Definitions:

Four Times

A phrase indicating a quantity or occurrence that is fourfold in number or frequency.

Two Times

Referring to an occurrence or action happening twice or a multiplication by two.

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Psychological conditions characterized by a disturbance in an individual's emotional state, which can significantly impact daily functioning.

Neurotic Disorders

Mental disorders characterized by anxiety, depression, or other feelings of distress that are not due to psychosis.