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

Transcript text: What are the amplitude and period of $y=2 \sin \left(\frac{x}{3}\right)$ ?

Solution

Solution Steps

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

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.
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 $.

Step 1: Determine the Amplitude

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: \[ \text{Amplitude} = |2| = 2 \]

Step 2: Determine the Period

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: \[ \text{Period} = \frac{2\pi}{\frac{1}{3}} = 6\pi \]