Question

The graph of $y=\cot \left(\frac{x}{2}\right)$ is given. Find the period and range of the function.

• A. Period: $2\pi$
  
  Range: $R$
• B. Period: $\frac{\pi }{2}$
  
  Range: $R$
• C. Period: $2\pi$
  
  Range: $R-\left\{0\right\}$
• D. Period: $\frac{\pi }{2}$
  
  Range: $R-\left\{0\right\}$

Answer 1

The correct option is A Period: $2\pi$


Range: $R$
From the given graph,

we can see that the graph is repeating itself after a period of $2\pi$ and the range is the same as that of $\cot$ function which is $R.$