Find the Exact Value tan((9pi)/2)

Problem

tan((9*π)/2)

Solution

1. Identify the angle in the expression, which is (9*π)/2

2. Simplify the angle by finding its coterminal equivalent within the interval [0,2*π) by subtracting multiples of 2*π

3. Calculate the subtraction: (9*π)/2−4*π=(9*π)/2−(8*π)/2=π/2

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

5. Evaluate the sine and cosine at the coterminal angle π/2 where sin(π/2)=1 and cos(π/2)=0

6. Determine the value of the fraction 1/0 which is undefined.

Final Answer

tan((9*π)/2)=Undefined

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