Chapter 8.5, Problem 34AYU

To determine

To find: The expression of each product as sum and to graph the given function using the method of adding $y\text{-coordinates}$.

Answer to Problem 34AYU

$F\left(x\right) = \text{sin}3x\text{sin}x = \frac{1}{2}\left[\text{cos}2x - \text{cos}4x\right]$

Explanation of Solution

Given:

$F\left(x\right) = \text{sin}3x\text{sin}x$

Formula used:

$\text{sin}A\text{sin}B = \frac{1}{2}\left[\text{cos}\left(A - B\right) - \text{cos}\left(A + B\right)\right]$

Calculation:

$\text{sin}A\text{sin}B = \frac{1}{2}\left[\text{cos}\left(A - B\right) - \text{cos}\left(A + B\right)\right]$

$F\left(x\right) = \text{sin}3x\text{sin}x = \frac{1}{2}\left[\text{cos}\left(3x - x\right) - \text{cos}\left(3x + x\right)\right]$

$\text{sin}3x\text{sin}x = \frac{1}{2}\left[\text{cos}2x - \text{cos}4x\right]$

Graph of $F\left(x\right) = \text{sin}3x\text{sin}x$

The graph for $f\left(x\right) = \text{sin}3x\text{sin}x$ = $\frac{1}{2}\left[\text{cos}2x - \text{cos}4x\right]$ using the method of adding $y\text{-coordinates}$ is plotted above using the graphing calculator.