Question

What is the domain of y = sec(x)?

1. all real numbers
2. real numbers except npi + pi/2, where n is any integer
3. real numbers except n Pi where n is any integer
4 . real numbers except n Pi and n Pi+ Pi/2, where n is any integer

Answer 1

The domain of y = sec(x) excludes all points where cosine of x equals zero, which is at x = nπ + π/2 for any integer n, making it the correct choice for the function's domain.

Step-by-step explanation:

The function y = sec(x) is the reciprocal of the cosine function. Since the cosine of x equals zero at x = nπ + π/2, where n is any integer and secant is not defined at these points, the domain of y = sec(x) excludes these values.

Therefore, the correct domain for the secant function is: all real numbers except nπ + π/2, where n is any integer, because at these points, the function would require division by zero, which is undefined.