Find the Exact Value tan((17pi)/4)

Problem

tan((17*π)/4)

Solution

1. Identify the period of the tangent function, which is π

2. Subtract multiples of the period π from the angle to find a coterminal angle within the interval [0,π)

3. Calculate the number of full periods to remove:

(17*π)/4=4*π+π/4

4. Apply the periodic property tan(θ+n*π)=tan(θ) for any integer n

tan(4*π+π/4)=tan(π/4)

5. Evaluate the tangent of the reference angle π/4 using the unit circle or special triangles:

tan(π/4)=1

Final Answer

tan((17*π)/4)=1

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