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.