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

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

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

Step3: Calculate the period

Using the formula, the period $T=\frac{\pi}{\left|\frac{3}{5}\right|}=\frac{5\pi}{3}$.

Answer:

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