Question

determine the period of the following trigonometric function.
\\( y = \frac{1}{2} \cos\left(6\pi x - \frac{\pi}{3}\
ight) \\)

Explanation:

Step1: Recall cosine period formula

For $y = A\cos(Bx + C) + D$, period is $\frac{2\pi}{|B|}$.

Step2: Identify B value

Here, $B = 6\pi$.

Step3: Calculate period

$\frac{2\pi}{|6\pi|} = \frac{2\pi}{6\pi} = \frac{1}{3}$.

Answer:

$\frac{1}{3}$