The given cosine function is y = 3cos(4x).
To determine the amplitude, we look at the coefficient in front of the cosine function. In this case, the amplitude is the absolute value of that coefficient, which is:
- Amplitude: |3| = 3
Next, let’s find the period. The standard form of a cosine function is y = Acos(Bx), where:
- A is the amplitude.
- B dictates the period of the function.
The period of the cosine function can be calculated using the formula:
Period = (2π) / |B|
In our function, B is 4. Hence, the period is:
- Period: (2π) / |4| = π/2
So, to summarize:
- Amplitude: 3
- Period: π/2
This means the function oscillates between 3 and -3, with a complete cycle occurring every π/2 units along the x-axis.