Sine Graph Transform C654B5

1. **Problem Statement:** We want to understand the transformation of the graph of the sine function given by the equation $$y=\frac{1}{2}\sin x$$. 2. **Formula and Rules:** The general sine function is $$y=\sin x$$. When multiplied by a factor $$a$$, the function becomes $$y=a\sin x$$, which vertically stretches or compresses the graph. 3. **Transformation Explanation:** Here, $$a=\frac{1}{2}$$, which means the amplitude of the sine wave is scaled by $$\frac{1}{2}$$. 4. **Amplitude Change:** The amplitude of $$\sin x$$ is normally 1, so the new amplitude is $$\left|\frac{1}{2}\right|=\frac{1}{2}$$. 5. **Effect on Graph:** This compresses the graph vertically, making the peaks and troughs half as high and half as low compared to the original sine wave. 6. **Summary:** The graph of $$y=\frac{1}{2}\sin x$$ is the graph of $$y=\sin x$$ compressed vertically by a factor of $$\frac{1}{2}$$, with amplitude $$\frac{1}{2}$$ instead of 1. **Final answer:** The transformation is a vertical compression by a factor of $$\frac{1}{2}$$ on the sine graph.