Find the Exact Value tan(-(5pi)/2)

Problem

tan(−(5*π)/2)

Solution

1. Simplify the angle by adding multiples of 2*π (the period of the tangent function is π but 2*π represents a full rotation) to find a coterminal angle.

θ=−(5*π)/2+2*π

θ=−(5*π)/2+(4*π)/2

θ=−π/2

2. Identify the coordinates on the unit circle for the angle −π/2

(x,y)=(0,−1)

3. Apply the definition of the tangent function, which is the ratio of the y-coordinate to the x-coordinate.

tan(θ)=y/x

tan(−π/2)=(−1)/0

4. Determine the value based on the division. Since division by zero is undefined, the tangent of this angle does not exist.

Final Answer

tan(−(5*π)/2)=Undefined

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