Find the Exact Value tan(11/6*pi)

Problem

tan((11*π)/6)

Solution

1. Identify the reference angle by determining how far the angle is from the nearest multiple of π

(11*π)/6=2*π−π/6

Reference Angle=π/6

2. Determine the quadrant of the angle (11*π)/6 Since it is between (3*π)/2 and 2*π the angle lies in Quadrant IV.

3. Determine the sign of the tangent function in Quadrant IV. In this quadrant, x is positive and y is negative, so tan(θ) is negative.

4. Evaluate the tangent of the reference angle.

tan(π/6)=1/√(,3)

5. Rationalize the denominator of the reference value.

1/√(,3)⋅√(,3)/√(,3)=√(,3)/3

6. Combine the reference value with the correct sign from step 3.

tan((11*π)/6)=−√(,3)/3

Final Answer

tan((11*π)/6)=−√(,3)/3

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