Find the Exact Value tan((17pi)/6)

Problem

tan((17*π)/6)

Solution

1. Find the coterminal angle by subtracting multiples of 2*π (which is (12*π)/6 to bring the angle within the interval [0,2*π)

(17*π)/6−(12*π)/6=(5*π)/6

2. Identify the reference angle for (5*π)/6 in the second quadrant.

π−(5*π)/6=π/6

3. Determine the sign of the tangent function in the second quadrant.

Quadrant II⇒tan(θ)<0

4. Apply the reference angle and the sign to find the exact value.

tan((5*π)/6)=−tan(π/6)

5. Substitute the known value for tan(π/6) which is √(,3)/3

−tan(π/6)=−√(,3)/3

Final Answer

tan((17*π)/6)=−√(,3)/3

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