Final answer:
The value of tan(-9π) can be found by using the periodicity of the tangent function, which leads to a simplified expression tan(0), and the value is 0.
Step-by-step explanation:
The question asks to find the value of the trigonometric function tan(-9π) without the use of tables or calculators. To solve this, we have to recognize that the tangent function has a period of π, which means that tan(θ) = tan(θ + nπ) for any integer n. Since -9π is equivalent to -9π + 18π (which adds 9 full periods to the angle), we get 9π, and hence, tan(-9π) = tan(0), which equals 0.