Final answer:
The value of cos(9π/2) is 0, because cos(9π/2) simplifies to cos(π/2) due to the periodicity of the cosine function, and the cosine of π/2 (90 degrees) is 0.
Step-by-step explanation:
To find the value of the trigonometric function cos(9π/2), we want to know the cosine of an angle that is 9 halves of π. Since the cosine function has a period of π*2, angles that differ by a full cycle (multiples of π*2) will have the same cosine value. Therefore, we can simplify this by removing full cycles to determine the cosine of the remaining angle.
Focusing on 9π/2, we can see that it contains four full cycles of π*2 (since 8π/2 is 4π), plus an additional π/2. Hence, cos(9π/2) is the same as cos(π/2), because the cos function repeats every 2π. The cosine of π/2 which is 90 degrees, is 0. Therefore, cos(9π/2) = 0.