Rewrite the Following as a Product of Trigonometric Functions $\sin ( \mathrm { s } - \mathrm { t } )$

question 3

Multiple Choice

Rewrite the following as a product of trigonometric functions.
-Find $\sin ( \mathrm { s } - \mathrm { t } )$ given that $\cos \mathrm { s } = \frac { 1 } { 3 }$ , with $\mathrm { s }$ in quadrant $\mathrm { I }$ , and $\sin \mathrm { t } = \frac { 1 } { 4 }$ , with $\mathrm { t }$ in quadrant II.

• A) \(\frac { - 12 \sqrt { 30 } - 1 } { 2 }\)
• B) \(\frac { - 30 \sqrt { 2 } - 1 } { 12 }\)
• C) \(\frac { - 2 \sqrt { 30 } - 1 } { 12 }\)
• D) \(\frac { - 12 \sqrt { 2 } - 1 } { 30 }\)

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Definitions:

Naturalistic Theory

A theory that explains phenomena or knowledge in terms of natural causes and processes, as opposed to supernatural or spiritual explanations.

Disharmony

A state of conflict or disconnection among elements that are meant to work together, often leading to dysfunction or imbalance.

Yin/Yang Theory

A fundamental concept in Chinese philosophy and culture, describing how opposite or contrary forces are interconnected and complementary in the natural world.

Tao

A fundamental concept in Chinese philosophy and religion, usually translated as "the Way," denoting the natural order or a principle that is the source of everything.