Question

Find the value of the trigonometric function. If possible, give the exact value; otherwise, use a calculator to find an approximate value correct to five decimal places. sec(9π/2)

Answer 1

The value of sec(9π/2) is undefined because the cosine of 9π/2 (or π/2) is 0, and the secant function is the reciprocal of the cosine function.

Step-by-step explanation:

The question is asking to find the value of sec(9π/2), which is the secant of 9π/2 radians. To understand secant, it is important to know that secant is the reciprocal of the cosine function, so sec(θ) = 1/cos(θ). The radian measure 9π/2 is an odd multiple of π/2, and since the cosine function has a period of 2π, we can simplify this to cos(π/2), which is 0. As the reciprocal of 0 is undefined, sec(9π/2) is also undefined. Hence, there is no exact or approximate numerical value for sec(9π/2).