Find the Exact Value tan((9pi)/4)

Problem

tan((9*π)/4)

Solution

1. Identify the angle and its periodicity. The tangent function has a period of π meaning tan(θ)=tan(θ+n*π) for any integer n

2. Subtract multiples of π to find a coterminal angle within the standard range of [0,π)

(9*π)/4=2*π+π/4

3. Apply the periodicity property of the tangent function.

tan(2*π+π/4)=tan(π/4)

4. Evaluate the tangent of the reference angle π/4 (or 45 using the unit circle or special right triangles.

tan(π/4)=1

Final Answer

tan((9*π)/4)=1

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