Chapter 8.5, Problem 39AYU

In Problems 25-32, use the method of adding $y\text{-coordinates}$ to graph each function.

$g(x)=\sin x+\sin (2x)$

To determine

To graph: Graph the function using the method of adding $\text{y}$ coordinates.

Answer to Problem 39AYU

Explanation of Solution

Given:

$f\left(x\right) = \text{sin}x + \text{sin}2x$

Graph:

Graph of $f\left(x\right) = \text{sin}x + \text{sin}2x$

Interpretation:

The graph for $f\left(x\right) = \text{sin}x + \text{sin}\left(2x\right)$ using the method of adding $\text{y}$ coordinates is plotted above. The set of points obtained by substitution are shown below.

$\begin{array}{llllll}x\hfill & 0\hfill & \text{π}/2\hfill & \text{π}\hfill & 3\text{π}/2\hfill & 2\text{π}\hfill \\ \text{sin}2x\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill \\ \text{sin}(x)\hfill & 0\hfill & 1\hfill & 0\hfill & -1\hfill & 0\hfill \\ f(x)\hfill & 0\hfill & 1\hfill & 0\hfill & -1\hfill & 0\hfill \end{array}$

Points for graph $\left(0,\text{ 0}\right)\left(\frac{\pi }{2},1\right)(\pi ,0)\left(\frac{3\pi }{2},-1\right)(2\pi ,0)$