Evaluate Without Using a Calculator $\sec \beta$ , If $\sin \beta = - \frac { 5 } { 10 }$

question 243

Multiple Choice

Evaluate without using a calculator.
- $\sec \beta$ , if $\sin \beta = - \frac { 5 } { 10 }$ and $\tan \theta > 0$

• A) \(\frac { \sqrt { 10 } } { 5 }\)
• B) \(- \frac { 10 \sqrt { 75 } } { 75 }\)
• C) \(- \frac { \sqrt { 75 } } { 10 }\)
• D) \(- \frac { 5 \sqrt { 75 } } { 75 }\)

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Definitions:

Catalytic Base

A substance that increases the rate of a chemical reaction by providing an alternative reaction pathway with lower activation energy, and which participates in the reaction as a base (accepting protons).

2-methylcyclohexanone

An organic compound consisting of a six-membered ring with a ketone functional group and a methyl group attached.

Enolate

An ion formed by the deprotonation of an alpha carbon of a carbonyl compound, involved in many important organic reactions.

Carbonyl

A functional group characterized by a carbon atom double-bonded to an oxygen atom (C=O).