Find the Exact Value tan(-pi/3)

Problem

tan(−π/3)

Solution

1. Identify the property for negative angles in the tangent function. Since tangent is an odd function, use the identity tan(−θ)=−tan(θ)

tan(−π/3)=−tan(π/3)

2. Determine the value of tan(π/3) using the unit circle or special right triangles. For an angle of π/3 (60, the coordinates are (1/2,√(,3)/2)

tan(π/3)=sin(π/3)/cos(π/3)

3. Substitute the values for sine and cosine.

tan(π/3)=√(,3)/2/1/2

4. Simplify the fraction to find the tangent of the positive angle.

tan(π/3)=√(,3)

5. Apply the negative sign from the first step to find the final result.

−tan(π/3)=−√(,3)

Final Answer

tan(−π/3)=−√(,3)

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