Use Implicit Differentiation to Find an Equation of the Tangent $y \sin 3 x = x \cos 3 y , \left( \frac { \pi } { 3 } , \frac { \pi } { 6 } \right)$

question 72

Multiple Choice

Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
$y \sin 3 x = x \cos 3 y , \left( \frac { \pi } { 3 } , \frac { \pi } { 6 } \right)$

• A) \(y = \frac { x } { 2 }\)
• B) \(y = 2 x - \frac { 3 \pi } { 3 }\)
• C) \(y = - \frac { x } { 2 } + \frac { \pi } { 2 }\)
• D) \(y = \frac { x } { 6 }\)
• E) \(y = \frac { x } { 3 } + \frac { \pi } { 6 }\)

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Definitions:

Red-Sensitive Cones

Photoreceptor cells in the retina that are particularly responsive to red wavelengths of light, playing a critical role in color vision.

Normal Color Vision

The ability to perceive colors accurately and differentiate between them, based on normal functioning of the cone cells in the retina.

Critical Period

A specific time in development during which an organism is particularly sensitive to environmental influences, outside of which such learning is significantly more difficult or even impossible.

Sensory Restriction

The limitation of normal sensory input, such as sight or hearing, which can lead to changes in perception or psychological state.