Question

determine the period of the following trigonometric function. $y = 4\sin\left(\dfrac{2\pi x}{3} + \dfrac{5}{6}\
ight) + 3$

Explanation:

Step1: Recall sine function period formula

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

Step2: Identify B value

Here, $B = \frac{2\pi}{3}$.

Step3: Calculate period

$\frac{2\pi}{|\frac{2\pi}{3}|} = \frac{2\pi \times 3}{2\pi} = 3$.

Answer:

3