Use the Fundamental Identities to Find the Value of the Trigonometric

question 138

Multiple Choice

Use the fundamental identities to find the value of the trigonometric function.
-Find $\cot \theta$ if $\csc \theta = \frac { \sqrt { 17 } } { 4 }$ and $\tan \theta > 0$ .

• A) \(\frac { \sqrt { 17 } } { 17 }\)
• B) \(\frac { 1 } { 4 }\)
• C) 4
• D) \(\sqrt { 17 }\)

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Definitions:

Pyrene

A polycyclic aromatic hydrocarbon (PAH) consisting of four fused benzene rings, resulting in a flat aromatic system.

Huckel Rule

A rule that helps predict the aromaticity of planar rings based on the count of pi electrons, stating that aromatic compounds must have 4n+2 pi electrons.

Aromatic

Refers to molecules that contain one or more planar rings of atoms with delocalized pi electron systems, typically associated with increased stability.

Antiaromatic

Compounds that have a cyclic, planar arrangement of atoms with 4n electrons that destabilize the molecule.