Use the Definitions (Not a Calculator) to Evaluate the Six $\frac { 3 \pi } { 2 }$

question 17

Multiple Choice

Use the definitions (not a calculator) to evaluate the six trigonometric functions of the given angle: $\frac { 3 \pi } { 2 }$

• A) \(\cos \frac { 3 \pi } { 2 } = 0\) , \(\sin \frac { 3 \pi } { 2 } = - 1\) , \(\tan \frac { 3 \pi } { 2 }\) is undefined, \(\sec \frac { 3 \pi } { 2 }\) is undefined, \(\cot \frac { 3 \pi } { 2 } = 0\) , \(\csc \frac { 3 \pi } { 2 } = - 1\) .
• B) \(\cos \frac { 3 \pi } { 2 } = - 1\) , \(\sin \frac { 3 \pi } { 2 } = 1\) , \(\tan \frac { 3 \pi } { 2 } = 0\) , \(\sec \frac { 3 \pi } { 2 } = - 1\) , \(\cot \frac { 3 \pi } { 2 }\) is undefined, \(\csc \frac { 3 \pi } { 2 }\) is undefined.
• C) \(\cos \frac { 3 \pi } { 2 } = 1\) , \(\sin \frac { 3 \pi } { 2 } = 1\) , \(\tan \frac { 3 \pi } { 2 }\) is undefined, \(\sec \frac { 3 \pi } { 2 }\) is undefined, \(\cot \frac { 3 \pi } { 2 } = 0\) , \(\csc \frac { 3 \pi } { 2 } = - 1\) .
• D) \(\cos \frac { 3 \pi } { 2 } = - \frac { 1 } { 2 }\) , \(\sin \frac { 3 \pi } { 2 } = \frac { \sqrt { 3 } } { 2 }\) , \(\tan \frac { 3 \pi } { 2 } = 0\) , \(\sec \frac { 3 \pi } { 2 } = - 1\) , \(\cot \frac { 3 \pi } { 2 }\) is undefined, \(\csc \frac { 3 \pi } { 2 }\) is undefined.
• E) \(\cos \frac { 3 \pi } { 2 } = - \frac { 1 } { 2 }\) , \(\sin \frac { 3 \pi } { 2 } = \frac { \sqrt { 3 } } { 2 }\) , \(\tan \frac { 3 \pi } { 2 }\) is undefined, \(\sec \frac { 3 \pi } { 2 }\) is undefined, \(\cot \frac { 3 \pi } { 2 } = 0\) , \(\csc \frac { 3 \pi } { 2 } = - 1\) .

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Definitions:

Economic Profit

The difference between total revenue and total costs, including both explicit and implicit costs, representing the financial gain exceeding the opportunity costs of resources.

MR = MC

An economic principle stating that the maximum profit occurs where marginal revenue equals marginal cost, guiding firms on the optimal level of output.

Output

The total amount of goods or services produced by a firm, industry, or economy within a given period.

Short-Run Supply

The supply of goods that varies with changes in price in the short term, where at least one factor of production is fixed.