In the equation y = 3 sin x, the amplitude and period can be determined by analyzing the properties of the sine function.
The general form of a sinusoidal function is y = A sin(Bx + C) + D, where A represents the amplitude, B represents the frequency (or angular frequency), C represents the phase shift, and D represents the vertical shift.
For the given equation y = 3 sin x:
- The coefficient 3 represents the amplitude. Therefore, the amplitude of the function is 3.
- Since there is no coefficient multiplying the x variable, the frequency (B) is 1, which means there is one complete period in a 2π interval.
- The phase shift (C) and vertical shift (D) are both absent in this equation, indicating no phase shift or vertical shift.
Therefore, the amplitude of y = 3 sin x is 3, and the period of the function is 2π.