Use a Sum or Difference Identity to Find the Exact $\sin ( \mathrm { s } - \mathrm { t } )$

question 179

Multiple Choice

Use a sum or difference identity to find the exact value.
-Find $\sin ( \mathrm { s } - \mathrm { t } )$ given that $\cos \mathrm { s } = \frac { 1 } { 3 }$ , with $\mathrm { s }$ in quadrant $\mathrm { I }$ , and $\sin t = - \frac { 1 } { 2 }$ , with $\mathrm { t }$ in quadrant IV.

• A) \(\frac { \sqrt { 3 } - 2 \sqrt { 2 } } { 6 }\)
• B) \(\frac { 2 \sqrt { 6 } + 1 } { 6 }\)
• C) \(\frac { \sqrt { 3 } + 2 \sqrt { 2 } } { 6 }\)
• D) \(\frac { 2 \sqrt { 6 } - 1 } { 6 }\)

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Definitions:

Additional Bakers

Implies an increase in the number of bakers in a market or industry, potentially increasing the supply of baked goods.

Local Bakery

A nearby place that specializes in baking and selling bread, pastries, cakes, and other baked goods.

Long-Run Adjustment

Economic processes or actions that firms take over time to adjust to market conditions, including changes in production capacity or entering and exiting markets.

Foreign Competition

The competitive pressure that domestic companies face from products and services offered by foreign entities in the same market.