Find the Exact Value tan(-(3pi)/2)

Problem

tan(−(3*π)/2)

Solution

1. Identify the angle in the expression, which is −(3*π)/2 radians.

2. Find a coterminal angle by adding 2*π to the negative angle to locate its position on the unit circle.

−(3*π)/2+2*π=π/2

3. Determine the coordinates on the unit circle for the angle π/2 which are (x,y)=(0,1)

4. Apply the definition of the tangent function, which is tan(θ)=y/x

tan(π/2)=1/0

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

Final Answer

tan(−(3*π)/2)=Undefined

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