1) Find the period and the amplitude.
y= 3 sin 2x
Please explain!!! I do not know how to do this.
The amplitude is how far y can increase above (or decrease below) the average value. The average value is zero. The maximum value is 3. The amplitude is therefore 3.
The period is how much x must increase in fr y to return to the original value (regardless of x).
2x must increase by 2 pi for that to happen. Therefore the period is pi
To find the period and amplitude of the given function, you need to understand the properties of trigonometric functions, specifically the sine function.
The general form of a sine function is given as follows: y = A sin(Bx + C) + D
In this case, the given function is y = 3 sin 2x. We can see that the amplitude (A) is 3, and the coefficient of x (B) is 2. The other parameters, C and D, are not present in our given function.
The amplitude (A) represents the maximum vertical distance that the function oscillates from its midline. In this case, the amplitude is 3, which means the function oscillates between y = -3 and y = 3.
The period of a sine function is the distance between two consecutive peaks or troughs (or equivalently, the distance between two consecutive complete cycles). The period can be determined using the formula:
Period = 2π/B
Since B = 2 in our function, we can compute the period as follows:
Period = 2π/2 = π
Hence, the period of the function y = 3 sin 2x is π, and the amplitude is 3.
To find the period and amplitude of the function y = 3 sin 2x, we need to understand the formula for the sine function and its relationship to the period and amplitude.
The general formula for the sine function is y = A sin (Bx + C), where:
- A represents the amplitude of the function (the distance from the centerline to the maximum or minimum point)
- B determines the period of the function (the distance between two repeating patterns)
- C is a phase shift (which we won't consider in this particular case, as there is no phase shift).
In your given function, y = 3 sin 2x, the amplitude is already given as 3. So, we only need to find the period.
To determine the period, we can use the formula:
Period (T) = 2π / |B|
In our case, B = 2, so we can substitute this value into the formula:
T = 2π / |2|
Since |2| equals 2, the period becomes:
T = 2π / 2
T = π
Therefore, the period of the function y = 3 sin 2x is π, and the amplitude is 3.