Find the Exact Value tan(-(4pi)/3)

Problem

tan(−(4*π)/3)

Solution

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

tan(−(4*π)/3)=−tan((4*π)/3)

2. Determine the reference angle for (4*π)/3 Since (4*π)/3 is in the third quadrant (Q*I*I*I, the reference angle is θ′=(4*π)/3−π

θ′=π/3

3. Determine the sign of the tangent function in the third quadrant. In Q*I*I*I tangent is positive.

tan((4*π)/3)=tan(π/3)

4. Evaluate the tangent of the reference angle using the unit circle or special triangles.

tan(π/3)=√(,3)

5. Substitute the value back into the expression from step 1.

−tan((4*π)/3)=−√(,3)

Final Answer

tan(−(4*π)/3)=−√(,3)

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