Determine All Solutions of the Equation in Radians $\cos ( s + t )$

question 306

Multiple Choice

Determine all solutions of the equation in radians.
-Find $\cos ( s + t )$ given that $\sin s = - \frac { 1 } { 2 }$ , with $s$ in quadrant IV, and $\sin t = \frac { 1 } { 4 }$ , with $t$ in quadrant II.

• A) \(- \frac { 4 \sqrt { 3 } + \sqrt { 15 } } { 11 }\)
• B) \(\frac { 1 + 3 \sqrt { 5 } } { 8 }\)
• C) \(\frac { 4 \sqrt { 3 } - \sqrt { 15 } } { 11 }\)
• D) \(\frac { 1 - 3 \sqrt { 5 } } { 8 }\)

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Definitions:

Monopolistic Competition

A market structure where many companies sell products that are similar but not identical, allowing for competition on factors other than just price, such as branding and quality.

Economics

Social science that analyzes the choices people and governments make in allocating scarce resources.

Substitute Goods

Products or services that can serve as replacements for each other, satisfying similar customer needs or desires.

Macroeconomic Effect

Refers to the large-scale impacts on an economy, including changes in inflation, unemployment, gross domestic product, and national income.