Use the Trigonometric Substitution $x = 8 \sec ( \theta )$

question 89

Multiple Choice

Use the trigonometric substitution $x = 8 \sec ( \theta )$ to write the expression $\sqrt { x ^ { 2 } - 64 }$ as a trigonometric function of $\theta$ , where $0 < \theta < \frac { \pi } { 2 }$ .

• A) \(8 \tan ( \theta )\)
• B) \(64 \tan ( \theta )\)
• C) \(64 \sec ( \theta )\)
• D) \(8 \sec ( \theta )\)
• E) \(8 \sec ( \theta ) - 1\)

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Definitions:

Sex Pheremones

Chemical substances secreted by individuals of a species to attract members of the opposite sex, playing a crucial role in mating behaviors.

Sp Hybridized

Describes an atom (usually carbon) with two sp hybrid orbitals formed from the mixing of one s and one p orbital, resulting in linear geometry.

CCC Bond Angle

The angle formed between two carbon-hydrogen bonds and a carbon-carbon bond within a molecule, typically around 109.5 degrees in sp3 hybridized carbon atoms.

Coplanar Atoms

Atoms that are in the same molecular plane, contributing to the overall geometry of a molecule.