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=2sin(3x):
Amplitude: The amplitude of a sine function y=Asin(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=Asin(Bx) is given by B2π. Here, B=31, so the period is 312π=6π.
Step 1: Determine the Amplitude
The amplitude of the function y=2sin(3x) 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
Step 2: Determine the Period
The period of the function y=2sin(3x) is given by:
Period=B2π
where B is the coefficient of x inside the sine function. Here, B=31. Therefore, the period is:
Period=312π=6π
Final Answer
The amplitude is 2 and the period is 6π.
Amplitude=2Period=6π
The correct answer is the first option: The amplitude is 2 and the period is 6π.