Find the period and the amplitude of the periodic function.
y=-4 cos 8x
It's B for the Connexus Test, just took it.
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Period: The period of a cosine function is given by 2π divided by the coefficient of x. In this case, the coefficient of x is 8, so the period is 2π/8, which simplifies to π/4.
Amplitude: The amplitude of a cosine function is the absolute value of the coefficient in front of the cosine term. In this case, the coefficient is -4, so the amplitude is 4.
So, the period of the function is π/4 and the amplitude is 4. But hey, don't worry, I'm sure there's a cosine-able explanation for all this!
To find the period and amplitude of the function y = -4cos(8x), we need to understand the properties of a cosine function.
1. Amplitude:
The amplitude refers to the maximum displacement from the mean position or the midline of the graph. In this case, the amplitude is the absolute value of the coefficient of the cosine function, which is 4. Therefore, the amplitude is 4.
2. Period:
The period refers to the length of one complete cycle of the function or the distance between two consecutive identical points on the graph. To find the period, we'll use the formula:
Period (T) = 2π / |B|
In this case, the coefficient of x in the cosine function is 8, so we'll use |8| in the formula.
T = 2π / |8|
T = π / 4
Therefore, the period of the function y = -4cos(8x) is π/4, or approximately 0.7854 units.