Final answer:
The exact value of tan(-π/3) is -√3, derived by using the odd property of the tangent function and its known value at 60 degrees or π/3 radians.
Step-by-step explanation:
To find the exact value of the trigonometric function tan (-π/3), we should recall the properties of the tangent function and its symmetry. The tangent function is odd, which means tan(-θ) = -tan(θ). Hence, we can say that tan (-π/3) is the negative of tan (π/3).
Now, evaluating tan (π/3), we can use the exact values from the unit circle where π/3 radians correspond to 60 degrees. The tangent of 60 degrees is √3. Therefore, tan (-π/3) = -√3.
The value of -√3 is the exact value for tan(-π/3) which is derived from the inherent symmetry of the tangent function and its value at 60 degrees or π/3 radians.