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2. Determinar:
● El periodo
● La amplitud
● El rango
● El dominio
De las siguientes funciones.

To determine the characteristics of the given trigonometric function, let's analyze the graph step-by-step:

1. **Period**: The period of a trigonometric function is the distance on the x-axis over which the function completes one full cycle. From the graph, it appears that the function completes one cycle between \( -\pi \) and \( \pi \). Therefore, the period is \( 2\pi \).

2. **Amplitude**: The amplitude is the maximum distance of the wave from the midline (usually the x-axis). From the graph, the function reaches a maximum of \( 1 \) and a minimum of \( -1 \). Therefore, the amplitude is \( 1 \).

3. **Range**: The range of the function is the set of all possible y-values. Since the graph oscillates between \( -1 \) and \( 1 \), the range is \([-1, 1]\).

4. **Domain**: The domain of a trigonometric function is usually all real numbers unless otherwise restricted. The graph doesn't show any restrictions, so the domain is all real numbers, \((-\infty, \infty)\).

Here is a summary:
- **Period**: \( 2\pi \)
- **Amplitude**: \( 1 \)
- **Range**: \([-1, 1]\)
- **Domain**: \((-\infty, \infty)\)

Would you like more details on these calculations, or do you have any questions?

### Related Questions:
1. How do you find the period of more complex trigonometric functions?
2. What is the effect of different coefficients on the amplitude of a function?
3. How would the graph change if the amplitude were doubled?
4. What happens to the period if the function is modified by a horizontal scaling factor?
5. How can you determine the phase shift from the graph of a trigonometric function?

### Tip:
Remember, the period of a trigonometric function \( y = a\sin(bx) \) or \( y = a\cos(bx) \) is given by \( \frac{2\pi}{|b|} \), where \( b \) affects the frequency and the amplitude \( a \) affects the height of the wave.

Learn how to determine the period, amplitude, range, and domain of trigonometric functions with a step-by-step analysis. This problem covers key concepts in trigonometry, including period calculation and amplitude determination. Suitable for high school students in Grades 11-12.

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