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

Problem

tan(−(7*π)/6)

Solution

1. Apply the odd function property of the tangent function, which states that tan(−θ)=−tan(θ)

−tan((7*π)/6)

2. Identify the reference angle for (7*π)/6 Since (7*π)/6=π+π/6 the angle is in the third quadrant (Quadrant III) and the reference angle is π/6

Reference Angle=π/6

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

tan((7*π)/6)=tan(π/6)

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

tan(π/6)=√(,3)/3

5. Combine the results by applying the negative sign from the first step to the value found.

−(√(,3)/3)

Final Answer

tan(−(7*π)/6)=−√(,3)/3

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