Find the Exact Value of the Expression Using the Provided $\sin ( s - t )$

question 459

Multiple Choice

Find the exact value of the expression using the provided information.
-Find $\sin ( s - t )$ given that $\sin s = - \frac { 1 } { 2 }$ , with $s$ in quadrant $I V$ , and $\sin t = \frac { 1 } { 4 }$ , with $t$ in quadrant II.

• A) \(\frac { - \sqrt { 15 } + \sqrt { 3 } } { 8 }\)
• B) \(\frac { \sqrt { 15 } + \sqrt { 3 } } { 8 }\)
• C) \(\frac { \sqrt { 15 } - \sqrt { 3 } } { 8 }\)
• D) \(\frac { - \sqrt { 15 } - \sqrt { 3 } } { 8 }\)

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Definitions:

Physical Laws

Fundamental principles that describe and predict the conditions under which physical events occur, usually expressed in mathematical form.

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Energy that is concentrated and easily transformed into other forms of energy, such as electricity and gasoline, with a high efficiency rate.

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Proposed explanations for a phenomenon, based on observation, which can be tested through experimentation or observation.

Deductive Reasoning

A logical process in which a conclusion follows necessarily from the set of premises provided, moving from general principles to specific instances.