Questions: What are the amplitude and period of y=2 sin (x/3) ?

Solution Steps

To determine the amplitude and period of the function $y = 2 \sin \left(\frac{x}{3}\right)$:

1. Amplitude: The amplitude of a sine function $y = A \sin(Bx)$ is given by the absolute value of the coefficient $A$. Here, $A = 2$, so the amplitude is 2.
2. Period: The period of a sine function $y = A \sin(Bx)$ is given by $\frac{2\pi}{B}$. Here, $B = \frac{1}{3}$, so the period is $\frac{2\pi}{\frac{1}{3}} = 6\pi$.

The amplitude of the function $y = 2 \sin \left(\frac{x}{3}\right)$ is given by the absolute value of the coefficient of the sine function. Here, the coefficient is 2. Therefore, the amplitude is: $$\text{Amplitude} = |2| = 2$$

The period of the function $y = 2 \sin \left(\frac{x}{3}\right)$ is given by: $$\text{Period} = \frac{2\pi}{B}$$ where $B$ is the coefficient of $x$ inside the sine function. Here, $B = \frac{1}{3}$. Therefore, the period is: $$\text{Period} = \frac{2\pi}{\frac{1}{3}} = 6\pi$$

Final Answer