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 $T=\frac{\pi}{|B|}$.

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

Substitute $B=\frac{3}{5}$ into the period - formula $T=\frac{\pi}{|B|}$. So $T=\frac{\pi}{\left|\frac{3}{5}\right|}=\frac{5\pi}{3}$.

Answer:

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