Question

question 13 of 30
what are the domain and range of ( y=cot x ) ? select one choice for domain and one for range.
a. domain: all real numbers
b. range ( -1 leq y leq 1 )
c. range: all real numbers
d. domain ( x
eq n pi )

Explanation:

Step1: Analyze domain of cot x

$\cot x = \frac{\cos x}{\sin x}$. Denominator $\sin x = 0$ when $x = n\pi$ (n integer). So domain is $x
eq n\pi$.

Step2: Analyze range of cot x

As $x$ approaches $0^+$, $\cot x$ approaches $+\infty$; as $x$ approaches $\pi^-$, $\cot x$ approaches $-\infty$. It covers all real numbers.

Answer:

D. Domain: $x
eq n\pi$, C. Range: All real numbers