The function \( y = \sin(2x) \) is a trigonometric function that describes a sine wave. Here's some important information about it:

### 1. **Amplitude:**
   - The amplitude of \( y = \sin(2x) \) is 1. This means the maximum value of \( y \) is 1, and the minimum value is -1.

### 2. **Period:**
   - The period of the sine function is \( \frac{2\pi}{B} \), where \( B \) is the coefficient of \( x \). In this case, \( B = 2 \), so the period is \( \frac{2\pi}{2} = \pi \). This means the function repeats every \( \pi \) units.

### 3. **Frequency:**
   - The frequency is the reciprocal of the period, which is \( \frac{1}{\pi} \). This tells us how many cycles occur within a unit interval.

### 4. **Phase Shift:**
   - There is no phase shift in \( y = \sin(2x) \) since there is no horizontal translation term added to \( x \).

### 5. **Vertical Shift:**
   - There is no vertical shift since there is no constant added to the sine function.

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### Related Questions:
1. What is the derivative of \( y = \sin(2x) \)?
2. How does the function \( y = \sin(2x) \) compare to \( y = \sin(x) \)?
3. What is the integral of \( y = \sin(2x) \)?
4. How does the amplitude affect the graph of \( y = A \sin(2x) \)?
5. What are the zeros of the function \( y = \sin(2x) \)?

### Tip:
When solving trigonometric equations involving \( \sin(2x) \), remember that it completes its cycle in half the interval compared to \( \sin(x) \), which impacts the solutions' spacing.

Explore the sine function y = sin(2x) with details on its amplitude, period, frequency, phase shift, and vertical shift. Learn about its properties and comparisons to the standard sine function. Suitable for advanced high school students and anyone interested in trigonometry.

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