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

Problem

tan(−(11*π)/6)

Solution

1. Find a coterminal angle by adding 2*π to the given angle to locate its position within the standard 0 to 2*π range.

θ=−(11*π)/6+2*π

θ=−(11*π)/6+(12*π)/6

θ=π/6

2. Identify the reference angle and the quadrant. The angle π/6 is in the first quadrant, where all trigonometric functions are positive.

Reference Angle=π/6

3. Apply the tangent value for the known special angle π/6

tan(π/6)=sin(π/6)/cos(π/6)

tan(π/6)=(1/2)/(√(,3)/2)

4. Simplify the fraction by multiplying by the reciprocal.

tan(π/6)=1/√(,3)

5. Rationalize the denominator by multiplying the numerator and denominator by √(,3)

tan(π/6)=√(,3)/3

Final Answer

tan(−(11*π)/6)=√(,3)/3

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