Chapter 8.5, Problem 38AYU

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

$f(x)=\sin (2x)+cosx$

To determine

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

Answer to Problem 38AYU

Explanation of Solution

Given:

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

Graph:

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

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

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

Points for graph (0, 1), ($\frac{\text{π}}{2},$0), (π, –1), ($\frac{3\text{π}}{2}$, 0), (2π, 1)