Question

Identify the statement that follows directly from the given condition about x .

sinx=0

a. The graph of y=secx has a vertical asymptote.
b. The graph of y=cscx has a vertical asymptote.
c. The graph of y=cscx has a relative minimum at x.
d. The graph of y=secx has a relative minimum at x.

Answer 1

The statement that follows directly from the given condition, x.sinx=0, is (b) The graph of y=cscx has a vertical asymptote.

Step-by-step explanation:

The statement that follows directly from the given condition, x.sinx=0, is (b) The graph of y=cscx has a vertical asymptote.

To determine this, we need to understand that when the product of two numbers is zero, at least one of the numbers must be zero. Therefore, if sinx = 0, then x = 0 or x is a multiple of π (pi). In the graph of y = cscx, the function approaches infinity or negative infinity as x approaches any multiple of π. This indicates that there is a vertical asymptote at each x value that is a multiple of π.