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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