Question
What are the amplitude and period of y= 5 cos (x/4)
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Answers
GPT-4o mini
To determine the amplitude and period of the function \( y = 5 \cos\left(\frac{x}{4}\right) \), we can analyze the general form of the cosine function.
1. **Amplitude**: The amplitude of a cosine function \( y = A \cos(Bx) \) is given by the absolute value of \( A \). In this case, \( A = 5 \), so the amplitude is:
\[
\text{Amplitude} = |5| = 5
\]
2. **Period**: The period of a cosine function \( y = A \cos(Bx) \) is given by the formula \( \frac{2\pi}{|B|} \). In this case, we have \( B = \frac{1}{4} \), so we calculate the period as follows:
\[
\text{Period} = \frac{2\pi}{\left|\frac{1}{4}\right|} = 2\pi \times 4 = 8\pi
\]
In summary, for the function \( y = 5 \cos\left(\frac{x}{4}\right) \):
- Amplitude: \( 5 \)
- Period: \( 8\pi \)
1. **Amplitude**: The amplitude of a cosine function \( y = A \cos(Bx) \) is given by the absolute value of \( A \). In this case, \( A = 5 \), so the amplitude is:
\[
\text{Amplitude} = |5| = 5
\]
2. **Period**: The period of a cosine function \( y = A \cos(Bx) \) is given by the formula \( \frac{2\pi}{|B|} \). In this case, we have \( B = \frac{1}{4} \), so we calculate the period as follows:
\[
\text{Period} = \frac{2\pi}{\left|\frac{1}{4}\right|} = 2\pi \times 4 = 8\pi
\]
In summary, for the function \( y = 5 \cos\left(\frac{x}{4}\right) \):
- Amplitude: \( 5 \)
- Period: \( 8\pi \)