Find the Exact Value of the Expression $$\tan ^ { - 1 } \left[ \tan \left( - \frac { \pi } { 8 } \right) \right]$$

question 65

Multiple Choice

Find the exact value of the expression. Do not use a calculator.
- $$\tan ^ { - 1 } \left[ \tan \left( - \frac { \pi } { 8 } \right) \right]$$

• A) \(- 8 \pi\)
• B) \(\frac { \pi } { 8 }\)
• C) \(8 \pi\)
• D) \(- \frac { \pi } { 8 }\)

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Definitions:

Mixed Integer Linear Optimization Model

An optimization technique involving mathematical formulas that aim to find the best outcome in a model with both integer and continuous variables under linear relationships.

Nonlinear Optimization Model

This is a mathematical model involving an optimization problem where the objective function or any of the constraints are nonlinear.

Integer

A whole number that can be positive, negative, or zero, not including fractions or decimals.

Nonlinear Optimization Model

A mathematical problem solving framework designed to optimize a nonlinear objective function subject to nonlinear constraints.