The equation \( y = \cos(x) \) represents a cosine function, which is a periodic trigonometric function. Here are some key properties of the cosine function:

1. **Domain**: The function \( y = \cos(x) \) is defined for all real numbers, so the domain is \( (-\infty, \infty) \).
   
2. **Range**: The values of \( y = \cos(x) \) are between -1 and 1, inclusive. Hence, the range is \( [-1, 1] \).

3. **Periodicity**: The cosine function repeats its values every \( 2\pi \) units. So, the period of \( y = \cos(x) \) is \( 2\pi \).

4. **Amplitude**: The amplitude of the cosine function is 1, which is the maximum distance from the horizontal axis to the peaks of the wave.

5. **Key points**: The function passes through several important points:
   - \( \cos(0) = 1 \)
   - \( \cos(\pi/2) = 0 \)
   - \( \cos(\pi) = -1 \)
   - \( \cos(3\pi/2) = 0 \)
   - \( \cos(2\pi) = 1 \)

Would you like more details or have any specific questions?

Here are 5 related questions to explore:

1. What is the derivative of \( y = \cos(x) \)?
2. How do you find the integral of \( y = \cos(x) \)?
3. What transformations occur if you modify \( y = \cos(x) \) to \( y = 2\cos(x) \) or \( y = \cos(x - \pi/4) \)?
4. How does the graph of \( y = \cos(x) \) compare to \( y = \sin(x) \)?
5. What are the real-world applications of the cosine function?

**Tip**: The cosine function describes oscillatory behavior, making it useful in modeling waves, sound, and circular motion.

Explore the properties of the cosine function y = cos(x), including its domain, range, amplitude, and periodicity. Learn key points of the function, like cos(0) = 1 and cos(π) = -1. Ideal for students in Grades 9-12 studying trigonometry and periodic functions.

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