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

Problem

tan((11*π)/6)

Solution

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

2. Determine the reference angle. The reference angle (θ_r*e*ƒ) for an angle in Quadrant IV is calculated as 2*π−θ

(θ_r*e*ƒ)=2*π−(11*π)/6

(θ_r*e*ƒ)=π/6

3. Apply the tangent function to the reference angle. The value of tan(π/6) is √(,3)/3

4. Determine the sign of the result. In Quadrant IV, the tangent function is negative.

tan((11*π)/6)=−tan(π/6)

5. Substitute the known value to find the final result.

tan((11*π)/6)=−√(,3)/3

Final Answer

tan((11*π)/6)=−√(,3)/3

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