what is the domain of ( y = csc(x) )?\n\n○ all real numbers\n\n○ all real numbers except ( npi+\frac{pi}{2}…

what is the domain of ( y = csc(x) )?\n\n○ all real numbers\n\n○ all real numbers except ( npi+\frac{pi}{2} ), where ( n ) is any integer\n\n○ all real numbers except ( npi ), where ( n ) is any integer\n\n○ all real numbers greater than 1 or less than -1

what is the domain of ( y = csc(x) )?\n\n○ all real numbers\n\n○ all real numbers except ( npi+\frac{pi}{2} ), where ( n ) is any integer\n\n○ all real numbers except ( npi ), where ( n ) is any integer\n\n○ all real numbers greater than 1 or less than -1

Answer

Explanation:

Step1: Recall the definition of (y = \csc(x))

(\csc(x)=\frac{1}{\sin(x)}). The function (y = \csc(x)) is undefined when (\sin(x)=0).

Step2: Find when (\sin(x) = 0)

We know that (\sin(x)=0) when (x = n\pi), where (n\in\mathbb{Z}) ( (n) is any integer).

Answer:

all real numbers except (n\pi), where (n) is any integer.