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Use the Definitions (Not a Calculator) to Evaluate the Six 3π2\frac { 3 \pi } { 2 }

Question 17

Multiple Choice

Use the definitions (not a calculator) to evaluate the six trigonometric functions of the given angle: 3π2\frac { 3 \pi } { 2 }


A) cos⁡3π2=0\cos \frac { 3 \pi } { 2 } = 0 , sin⁡3π2=−1\sin \frac { 3 \pi } { 2 } = - 1 , tan⁡3π2\tan \frac { 3 \pi } { 2 } is undefined, sec⁡3π2\sec \frac { 3 \pi } { 2 } is undefined, cot⁡3π2=0\cot \frac { 3 \pi } { 2 } = 0 , csc⁡3π2=−1\csc \frac { 3 \pi } { 2 } = - 1 .
B) cos⁡3π2=−1\cos \frac { 3 \pi } { 2 } = - 1 , sin⁡3π2=1\sin \frac { 3 \pi } { 2 } = 1 , tan⁡3π2=0\tan \frac { 3 \pi } { 2 } = 0 , sec⁡3π2=−1\sec \frac { 3 \pi } { 2 } = - 1 , cot⁡3π2\cot \frac { 3 \pi } { 2 } is undefined, csc⁡3π2\csc \frac { 3 \pi } { 2 } is undefined.
C) cos⁡3π2=1\cos \frac { 3 \pi } { 2 } = 1 , sin⁡3π2=1\sin \frac { 3 \pi } { 2 } = 1 , tan⁡3π2\tan \frac { 3 \pi } { 2 } is undefined, sec⁡3π2\sec \frac { 3 \pi } { 2 } is undefined, cot⁡3π2=0\cot \frac { 3 \pi } { 2 } = 0 , csc⁡3π2=−1\csc \frac { 3 \pi } { 2 } = - 1 .
D) cos⁡3π2=−12\cos \frac { 3 \pi } { 2 } = - \frac { 1 } { 2 } , sin⁡3π2=32\sin \frac { 3 \pi } { 2 } = \frac { \sqrt { 3 } } { 2 } , tan⁡3π2=0\tan \frac { 3 \pi } { 2 } = 0 , sec⁡3π2=−1\sec \frac { 3 \pi } { 2 } = - 1 , cot⁡3π2\cot \frac { 3 \pi } { 2 } is undefined, csc⁡3π2\csc \frac { 3 \pi } { 2 } is undefined.
E) cos⁡3π2=−12\cos \frac { 3 \pi } { 2 } = - \frac { 1 } { 2 } , sin⁡3π2=32\sin \frac { 3 \pi } { 2 } = \frac { \sqrt { 3 } } { 2 } , tan⁡3π2\tan \frac { 3 \pi } { 2 } is undefined, sec⁡3π2\sec \frac { 3 \pi } { 2 } is undefined, cot⁡3π2=0\cot \frac { 3 \pi } { 2 } = 0 , csc⁡3π2=−1\csc \frac { 3 \pi } { 2 } = - 1 .

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