Question

The graph of $3$cosec $2x$ is given. What is the domain and period of the function?

• A. Domain: $R-\{\frac{n\pi }{4};n\in Z\}$.
  period: $\pi$.
• B. Domain: $R-\{\frac{n\pi }{4};n\in Z\}$.
  period: $2\pi$.
• C. Domain: $R-\{\frac{n\pi }{2};n\in Z\}$.
  period: $\pi$.
• D. Domain: $R-\{\frac{n\pi }{2};n\in Z\}$.
  period: $2\pi$.

Answer 1

The correct option is C Domain: $R-\{\frac{n\pi }{2};n\in Z\}$.

period: $\pi$.
From the graph given, we can see that the graph repeats after a period of $\pi$.
Also domain of the function will exclude the points where $\sin 2x$ will be zero.
$\Rightarrow$ the domain of the given function is $R-\{\frac{n\pi }{2};n\in Z\}$