Chapter 7.3, Problem 92AYU

In Problems 83-94, use a graphing utility to solve each equation. Express the solution(s) rounded to two decimal places.

$4\cos \left(3x\right)-e^x=1$, $x>0$

To determine

To find: Trigonometric equation in the form of $f\left(x\right)=4\cos \left(3x\right)-e^x=1\text{, }x>0$ using graphic utility and to express the solution up to two decimal places.

Answer to Problem 92AYU

The solution set using graphic utility $=\left\{-1.15,-0.62,0.38\right\}$.

Explanation of Solution

Given:

Trigonometric equation $f\left(x\right)=4\cos \left(3x\right)-e^x=1$.

Calculation:

$y=f\left(x\right)=4\cos \left(3x\right)-e^x=1$

Each solution of the equation is the $x\text{-coordinate}$ of the point of intersection of the graph of,

$y=f\left(x\right)=4\cos \left(3x\right)-e^x=1$

There are 3 intersections on the $x\text{-axis}$ of the graph of $y=f\left(x\right)=4\cos \left(3x\right)-e^x=1$.

The solution $\text{set }=\left\{-1.15\text{, }-0.62\text{, }0.38\right\}$.