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The equation provided is:

\[
y = \frac{4}{5} \cos \left( \frac{4x}{5} \right)
\]

To find the **period** and **amplitude**, follow these steps:

### 1. Amplitude:
For a cosine function of the form:

\[
y = A \cos(Bx)
\]

- The **amplitude** is the absolute value of \(A\). 
- Here, \(A = \frac{4}{5}\), so the **amplitude** is:

\[
\text{Amplitude} = \left| \frac{4}{5} \right| = \frac{4}{5}
\]

### 2. Period:
The period of a cosine function is calculated using the formula:

\[
\text{Period} = \frac{2\pi}{B}
\]

- In the equation \(y = \frac{4}{5} \cos \left( \frac{4x}{5} \right)\), the coefficient of \(x\) is \(\frac{4}{5}\), which is the value of \(B\).
- Substituting \(B = \frac{4}{5}\) into the period formula:

\[
\text{Period} = \frac{2\pi}{\frac{4}{5}} = 2\pi \times \frac{5}{4} = \frac{5\pi}{2}
\]

### Final Answers:
- **Amplitude**: \(\frac{4}{5}\)
- **Period**: \(\frac{5\pi}{2}\)

Would you like further details or have any other questions?

### Related Questions:
1. How does the period of a sine or cosine function change with different values of \(B\)?
2. What happens to the amplitude if \(A\) is negative in a trigonometric function?
3. How do you graph a cosine function with a fractional amplitude and period?
4. Can the same process be applied to find the period and amplitude for sine functions?
5. What does the phase shift represent in a trigonometric function?

### Tip:
For cosine or sine functions of the form \(y = A \cos(Bx + C)\), the phase shift can also be calculated as \(\frac{-C}{B}\), and it tells you how the graph shifts horizontally.

Find the period and amplitude. y = (4/5) cos(4x/5)

Learn how to calculate the period and amplitude for the function y = (4/5) cos(4x/5). This example covers trigonometric concepts such as amplitude and period, along with the key formulas used in solving this problem. Suitable for high school students in Grades 9-12.

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