1) Find the period and the amplitude.
y= 3 sin 2x
Please explain!!! I do not know how to do this.
To find the period and amplitude of the function y = 3 sin 2x, let's break it down step by step:
1) Period: The period is the distance between two consecutive peaks or troughs of a sinusoidal function. In general, for the standard sine function y = sin x, the period is 2π.
However, for the given function y = 3 sin 2x, there is a coefficient of 2 in front of the x. This coefficient affects the period. To find the period, you divide the standard period (2π) by the coefficient in front of x.
So, in this case, the coefficient is 2, which means the period is given by:
Period = (2π) / 2 = π
Therefore, the period of the given function is π.
2) Amplitude: The amplitude represents the maximum displacement from the midline (the x-axis) of a sinusoidal function. It is the absolute value of the coefficient in front of the sine or cosine function.
In the given function y = 3 sin 2x, the absolute value of the coefficient in front of sin 2x is 3. Therefore, the amplitude is 3.
In conclusion:
- The period of the function y = 3 sin 2x is π.
- The amplitude of the function y = 3 sin 2x is 3.