what is the period of the function $y = \\frac{3}{2}\\cot(\\frac{3}{5}x)+5$?\n$\\frac{\\pi}{5}$…

what is the period of the function $y = \\frac{3}{2}\\cot(\\frac{3}{5}x)+5$?\n$\\frac{\\pi}{5}$ units\n$\\frac{3\\pi}{5}$ units\n$\\frac{2\\pi}{3}$ units\n$\\frac{5\\pi}{3}$ units

what is the period of the function $y = \\frac{3}{2}\\cot(\\frac{3}{5}x)+5$?\n$\\frac{\\pi}{5}$ units\n$\\frac{3\\pi}{5}$ units\n$\\frac{2\\pi}{3}$ units\n$\\frac{5\\pi}{3}$ units

Answer

Explanation:

Step1: Recall cotangent period formula

The period of the cotangent function $y = A\cot(Bx - C)+D$ is given by $\frac{\pi}{|B|}$.

Step2: Identify the value of B

For the function $y=\frac{3}{2}\cot(\frac{3}{5}x)+5$, we have $B = \frac{3}{5}$.

Step3: Calculate the period

Using the formula $\frac{\pi}{|B|}$, we substitute $B=\frac{3}{5}$ to get $\frac{\pi}{\frac{3}{5}}=\frac{5\pi}{3}$.

Answer:

D. $\frac{5\pi}{3}$ units