Find the Exact Value of the Expression Using the Provided $\cos ( \mathrm { s } - \mathrm { t } )$

question 106

Multiple Choice

Find the exact value of the expression using the provided information.
-Find $\cos ( \mathrm { s } - \mathrm { t } )$ given that $\cos \mathrm { s } = - \frac { 1 } { 6 }$ , with $\mathrm { s }$ in quadrant III, and $\cos \mathrm { t } = - \frac { 3 } { 5 }$ , with $\mathrm { t }$ in quadrant III.

• A) \(\frac { - 3 + 4 \sqrt { 35 } } { 30 }\)
• B) \(\frac { 3 + 4 \sqrt { 35 } } { 30 }\)
• C) \(\frac { 3 - 4 \sqrt { 37 } } { 30 }\)
• D) \(\frac { 3 - 4 \sqrt { 35 } } { 30 }\)

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Definitions:

Transformational Rule

In linguistics, a rule that takes an input, such as a basic sentence structure, and transforms it into a new structure, often to express a different grammatical mood or voice.

Cognition

The mental processes involved in gaining knowledge and comprehension, including aspects like thinking, knowing, remembering, judging, and problem-solving.

Mental Processes

These refer to the internal cognitive activities that include thinking, perceiving, problem-solving, and information processing.

Cognitive Activity

Cognitive activity involves processes related to thinking, such as problem-solving, memory, decision-making, and perception, indicative of the mental action or process of acquiring knowledge and understanding.