Find the Exact Value tan((7pi)/6)

Problem

tan((7*π)/6)

Solution

1. Identify the quadrant of the angle (7*π)/6 Since π<(7*π)/6<(3*π)/2 the angle is in the third quadrant.

2. Determine the reference angle. For an angle in the third quadrant, the reference angle θ′ is calculated as θ−π

θ′=(7*π)/6−π

θ′=π/6

3. Determine the sign of the tangent function in the third quadrant. In the third quadrant, tangent is positive.

4. Evaluate the tangent of the reference angle. Using the unit circle or special triangles, find the value for π/6

tan(π/6)=1/√(,3)

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

1/√(,3)⋅√(,3)/√(,3)=√(,3)/3

Final Answer

tan((7*π)/6)=√(,3)/3

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