Let f(x) = 1+3sin2x be a function, determin the amplitude and the period of the function,
amplitude = 3
period = 2π/2 = π or 180°
To determine the amplitude and period of the function f(x) = 1 + 3 sin(2x), we can use the general form of the sine function: f(x) = A sin(Bx + C) + D.
In this case, A represents the amplitude, B represents the period, and C represents the phase shift.
1. Amplitude (A):
The amplitude of a sine function is the absolute value of the coefficient of the sine term. In this case, the coefficient is 3. Therefore, the amplitude (A) of our function f(x) is 3.
2. Period (B):
The period of a sine function can be determined using the formula: Period (T) = 2π / |B|. In our case, the coefficient of x in the sine term is 2, so |B| = 2.
Now we can calculate the period:
T = 2π / |B| = 2π / 2 = π.
Therefore, the period (B) of our function f(x) is π.
To summarize:
Amplitude (A) = 3
Period (B) = π