Use the Trigonometric Substitution to Rewrite the Algebraic Expression as a Trigonometric

question 43

Multiple Choice

Use the trigonometric substitution to rewrite the algebraic expression as a trigonometric function of $\theta$ , where $0 < x < \frac { \pi } { 2 }$ . $\sqrt { x ^ { 2 } + 25 } , x = 5 \tan \theta$

• A)- 5 sec\(\theta \)
• B)5 tan \(\theta \)
• C)25 sec \(\theta \)
• D)25 tan \(\theta \)
• E)5 sec\(\theta \)

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Definitions:

Hydrolysis

A chemical reaction involving the breaking of a bond in a molecule using water, common in the digestion of nutrients.

Fatty Acids

Long-chain hydrocarbons found in fats and oils, serving as major sources of energy, components of cell membranes, and precursors for bioactive signaling molecules.

Glycerol

A simple polyol compound that forms the backbone of triglycerides, which are the main constituents of body fat in humans and other animals.

Nucleotide

The basic building block of nucleic acids, such as DNA and RNA, consisting of a base (adenine, cytosine, guanine, thymine in DNA; adenine, cytosine, guanine, uracil in RNA), a molecule of sugar (deoxyribose in DNA and ribose in RNA), and a phosphate group.