Determine the amplitude of the function \( y=\frac{1}{2} \sin x \). Graph the function and \( y=\sin x \). The amplitude is (Simplify your answer.)

The amplitude of a sinusoidal function is determined by the coefficient in front of the sine (or cosine) term. For the function \( y = \frac{1}{2} \sin x \), the amplitude is \( \frac{1}{2} \). This means that the graph of this function oscillates between \( \frac{1}{2} \) and \( -\frac{1}{2} \), while the standard sine function \( y = \sin x \) has an amplitude of 1, oscillating between 1 and -1. To graph these functions, you would plot the points of \( y = \sin x \) from -1 to 1 on the vertical axis. Then, for \( y = \frac{1}{2} \sin x \), you would scale the sine wave down to oscillate between -0.5 and 0.5. This creates a smaller, more subtle wave that sits comfortably within the peaks and troughs of its louder sibling!