what is the period of the function f(x) = 1/2 csc(6x - 1)? a. 6π b. π/2 c. 2π d. π/3

Explanation:

Step1: Recall csc - function period formula

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

Step2: Identify the value of B

For the function $F(x)=\frac{1}{2}\csc(6x - 1)$, we have $B = 6$.

Step3: Calculate the period

Substitute $B = 6$ into the period formula $T=\frac{2\pi}{|B|}$. So $T=\frac{2\pi}{6}=\frac{\pi}{3}$.

Answer:

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