### Home > A2C > Chapter 8 > Lesson 8.2.3 > Problem8-143

8-143.

Based on your explorations in class, complete parts (a) through (c) below.

1. Describe what the graph of $y = 3 \operatorname { sin } ( \frac { 1 } { 2 } x )$ will look like compared to the graph of $y = \operatorname{sin} x$.

Is there a horizontal or vertical shift? Does the amplitude or period change?

$\text{The graph of }y = 3\text{sin} \left(\frac{1}{2}x\right)\text{ has an amplitude of 3 and a period of } 4\pi.$

2. Sketch both graphs on the same set of axes.

Since there is no horizontal or vertical shift, both graphs start at $\left(0,0\right)$.

3. Explain the similarities and differences between the two graphs.

See parts (a) and (b).

Use the eTool below to help answer the parts of the problem.
Click the link at right for the full version of the eTool: A2C 8-143 HW eTool