Question

The period of the function $g(x)=5\cot(\frac{\pi}{3}x+\frac{\pi}{6})+2$ is equal to

• A. 2
• B. 3
• C. 4
• D. 5
• E. 6

Answer 1

The Correct Option is B

The period of the cotangent function $\cot(x)$ is $\pi$. For a function of the form $\cot(kx + \phi)$, the period is given by: $$\text{Period} = \frac{\pi}{|k|}$$ In this case, the argument of the cotangent is $\frac{\pi}{3} x + \frac{\pi}{6}$, where $k = \frac{\pi}{3}$. Thus, the period of $g(x) = 5 \cot \left( \frac{\pi}{3} x + \frac{\pi}{6} \right) + 2$ is: $$\text{Period} = \frac{\pi}{\left| \frac{\pi}{3} \right|} = 3$$

The correct option is (B) : $3$