what is the period of the function y=-1/2 cos(3x)? \nπ/3 \n2π \nπ \n2π/3

Explanation:

Step1: Recall cosine - function period formula

The general form of a cosine function is $y = A\cos(Bx - C)+D$, and its period $T$ is given by $T=\frac{2\pi}{|B|}$.

Step2: Identify the value of B

For the function $y =-\frac{1}{2}\cos(3x)$, we have $B = 3$.

Step3: Calculate the period

Substitute $B = 3$ into the period formula $T=\frac{2\pi}{|B|}$, we get $T=\frac{2\pi}{|3|}=\frac{2\pi}{3}$.

Answer:

$\frac{2\pi}{3}$