Question

Given the graph of $y=\cot 2x;y\in R.$ Then select the correct statement:

• A. Period: $\pi /2$
• B. Period: $\pi$
• C. Domain: $R-n\pi ;n\in Z$
• D. Domain: $R-n\pi /2;n\in Z$

Answer 1

Answer: (A), (D)

Domain: $R-n\pi /2;n\in Z$

From the given graph of $\cot 2x:$


We can observe $\cot 2x$ is not defined for angles $x=-\pi /2,0,\pi /2,\pi ,3\pi /2$
$\therefore$ Domain of $\cot 2x$ is:
$D:R-n\pi /2,\forall n\in Z$

Also, for period we can can see the function value getting repated after every $\pi /2$ interval.
Hence, Period of $\cot 2x=\pi /2.$