Find the Exact Value tan((13pi)/3)

Problem

tan((13*π)/3)

Solution

1. Find a coterminal angle by subtracting multiples of 2*π until the angle is within the interval [0,2*π)

2*π=(6*π)/3

(13*π)/3−(6*π)/3=(7*π)/3

(7*π)/3−(6*π)/3=π/3

2. Identify the reference angle and the quadrant. The angle π/3 is in the first quadrant, where all trigonometric functions are positive.

tan((13*π)/3)=tan(π/3)

3. Evaluate the tangent using the known values for special angles.

tan(π/3)=√(,3)

Final Answer

tan((13*π)/3)=√(,3)

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