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We are tasked with writing a cosine function with the following characteristics:

1. **Amplitude (A)**: -10
2. **Period**: \( \frac{2\pi}{10} \)
3. **Phase Shift (ϕ)**: \( \frac{-\pi}{6} \)

We need to format the equation in the general form:
\[
A \cos \left( \omega \left( x - \frac{\phi}{\omega} \right) \right)
\]
where:
- \( A \) is the amplitude.
- \( \omega \) is the angular frequency, related to the period by the formula \( \omega = \frac{2\pi}{\text{Period}} \).
- \( \phi \) is the phase shift.

### Step-by-Step Solution:

1. **Amplitude (A)**: Given as -10, so \( A = -10 \).

2. **Period**: The period is given as \( \frac{2\pi}{10} \). The angular frequency \( \omega \) is calculated by using the formula:
   \[
   \omega = \frac{2\pi}{\text{Period}} = \frac{2\pi}{\frac{2\pi}{10}} = 10
   \]

3. **Phase Shift (ϕ)**: Given as \( \frac{-\pi}{6} \).

Now, plugging these values into the cosine function formula:

\[
y = -10 \cos \left( 10 \left( x - \frac{\frac{-\pi}{6}}{10} \right) \right)
\]

Simplifying the phase shift expression:

\[
y = -10 \cos \left( 10 \left( x + \frac{\pi}{60} \right) \right)
\]

### Final Answer:
\[
y = -10 \cos \left( 10 \left( x + \frac{\pi}{60} \right) \right)
\]

Would you like a more detailed breakdown or have any further questions? 

Here are some related questions:
1. How do you calculate the phase shift for sinusoidal functions?
2. What is the significance of negative amplitude in a cosine function?
3. How does the period of a function relate to its angular frequency?
4. What are the differences between sine and cosine in terms of phase shift?
5. How do you graph a cosine function with a phase shift and amplitude change?

**Tip**: For functions with phase shifts, remember that \( x - \phi \) means a shift to the right, while \( x + \phi \) means a shift to the left.

Write a cosine function with given characteristics: Amplitude = -10, Period = 2π/10, Phase Shift = -π/6

Learn how to write a cosine function with an amplitude of -10, a period of 2π/10, and a phase shift of -π/6. This problem covers essential trigonometry concepts, including amplitude, phase shift, and angular frequency. Suitable for high school students in Grades 10-12.

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