1/4sinx

The expression \( \frac{1}{4} \sin x \) represents a scaled version of the sine function.

Here are a few properties and transformations related to this expression:

1. Amplitude: The amplitude of the function \( \frac{1}{4} \sin x \) is \( \frac{1}{4} \). This means that the maximum value of \( \sin x \), which is 1, will now only reach \( \frac{1}{4} \).

2. Period: The period of \( \sin x \) is \( 2\pi \). The period does not change with the scaling factor, so the period of \( \frac{1}{4} \sin x \) is still \( 2\pi \).

3. Graph: When you graph \( y = \frac{1}{4} \sin x \), the wave will oscillate between \( -\frac{1}{4} \) and \( \frac{1}{4} \) along the y-axis.

4. Value at specific points:

   • \( x = 0 \): \( \frac{1}{4} \sin(0) = 0 \)
   • \( x = \frac{\pi}{2} \): \( \frac{1}{4} \sin\left(\frac{\pi}{2}\right) = \frac{1}{4} \)
   • \( x = \pi \): \( \frac{1}{4} \sin(\pi) = 0 \)
   • \( x = \frac{3\pi}{2} \): \( \frac{1}{4} \sin\left(\frac{3\pi}{2}\right) = -\frac{1}{4} \)
   • \( x = 2\pi \): \( \frac{1}{4} \sin(2\pi) = 0 \)

If you need further analysis or applications of this expression, such as derivatives, integrals, or specific equations, feel free to ask!