Find the Exact Value cot((3pi)/2)

Problem

cot((3*π)/2)

Solution

1. Identify the definition of the cotangent function in terms of sine and cosine.

cot(θ)=cos(θ)/sin(θ)

2. Substitute the given angle θ=(3*π)/2 into the definition.

cot((3*π)/2)=cos((3*π)/2)/sin((3*π)/2)

3. Determine the values of cosine and sine at (3*π)/2 radians (270 using the unit circle.

cos((3*π)/2)=0

sin((3*π)/2)=−1

4. Simplify the fraction by dividing the values.

0/(−1)=0

Final Answer

cot((3*π)/2)=0

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