Determine the Exact Value Of $\csc \theta$ When $\cot \theta = \frac { 20 } { 21 }$

question 217

Multiple Choice

Determine the exact value of $\csc \theta$ when $\cot \theta = \frac { 20 } { 21 }$ and $\csc \theta$ < 0.

• A) \(\csc \theta = - \frac { 11 } { 14 }\)
• B) \(\csc \theta = - \frac { 3 } { 2 }\)
• C) \(\csc \theta = - \frac { 58 } { 21 }\)
• D) \(\csc \theta = - \frac { 8 } { 21 }\)
• E) \(\csc \theta = - \frac { 29 } { 21 }\)

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Definitions:

Ossicles

Three tiny bones in the middle ear known as the malleus, incus, and stapes, which play a critical role in transmitting sound vibrations to the inner ear.

Place Theory

A theory that suggests that our perception of sound depends on where each component frequency produces vibrations along the basilar membrane of the cochlea.

Hermann von Helmholtz

A German physician and physicist who made significant contributions to the understanding of the physiology of vision, hearing, and electromagnetism.

Basilar Membrane

A core component of the cochlea in the inner ear, playing a crucial role in the sense of hearing by vibrating in response to sound.