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

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

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Solution Steps

To determine the amplitude and period of the function y=2sin(x3) y = 2 \sin \left(\frac{x}{3}\right) :

  1. Amplitude: The amplitude of a sine function y=Asin(Bx) y = A \sin(Bx) is given by the absolute value of the coefficient A A . Here, A=2 A = 2 , so the amplitude is 2.
  2. Period: The period of a sine function y=Asin(Bx) y = A \sin(Bx) is given by 2πB \frac{2\pi}{B} . Here, B=13 B = \frac{1}{3} , so the period is 2π13=6π \frac{2\pi}{\frac{1}{3}} = 6\pi .
Step 1: Determine the Amplitude

The amplitude of the function y=2sin(x3) 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: Amplitude=2=2 \text{Amplitude} = |2| = 2

Step 2: Determine the Period

The period of the function y=2sin(x3) y = 2 \sin \left(\frac{x}{3}\right) is given by: Period=2πB \text{Period} = \frac{2\pi}{B} where B B is the coefficient of x x inside the sine function. Here, B=13 B = \frac{1}{3} . Therefore, the period is: Period=2π13=6π \text{Period} = \frac{2\pi}{\frac{1}{3}} = 6\pi

Final Answer

The amplitude is 2 2 and the period is 6π 6\pi .

Amplitude=2 \boxed{\text{Amplitude} = 2} Period=6π \boxed{\text{Period} = 6\pi}

The correct answer is the first option: The amplitude is 2 and the period is 6π 6\pi .

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