Evaluate tan((3pi)/2)

Problem

tan((3*π)/2)

Solution

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

tan(θ)=sin(θ)/cos(θ)

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

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

3. Evaluate the sine and cosine values at the angle (3*π)/2 on the unit circle.

sin((3*π)/2)=−1

cos((3*π)/2)=0

4. Determine the value of the fraction by substituting the coordinates.

tan((3*π)/2)=(−1)/0

5. Conclude that since division by zero is undefined, the tangent of the angle does not exist.

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Final Answer

tan((3*π)/2)=undefined

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