Find the Exact Value tan(-(5pi)/6)

Problem

tan(−(5*π)/6)

Solution

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

tan(−(5*π)/6)=−tan((5*π)/6)

2. Identify the reference angle for (5*π)/6 Since the angle is in the second quadrant, the reference angle is π−(5*π)/6=π/6

Reference Angle=π/6

3. Determine the sign of the tangent function in the second quadrant. In Quadrant II, tangent is negative.

tan((5*π)/6)=−tan(π/6)

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

tan((5*π)/6)=−√(,3)/3

5. Combine the results by substituting this back into the expression from step 1.

−(−√(,3)/3)=√(,3)/3

Final Answer

tan(−(5*π)/6)=√(,3)/3

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