1) Find the period and the amplitude.
y= 3 sin 2x
Please explain!!!
To find the period and amplitude of the function y = 3 sin 2x, we need to understand what these terms mean.
The period of a sine function is the distance between two consecutive points that have the same value. It represents the length of one complete cycle of the function. The amplitude, on the other hand, refers to the maximum distance the function reaches from its mean value.
For the given function y = 3 sin 2x:
1. The amplitude is the coefficient of the sine function, which is 3 in this case. Therefore, the amplitude is 3.
2. The period can be calculated using the formula: P = 2π / |B|, where B is the coefficient of x in the sine function. In this case, B is 2. Thus, the period P = 2π / |2| = π.
So, the period is π and the amplitude is 3 for the function y = 3 sin 2x.