Question

Use a graphing utility to solve the equation on the interval $0\le x\le 2\mathrm{\pi }$. Approximate any solutions rounded to two decimal places.

$2\sin x+3\cos x=4x$

Short answer

The solution set is $\left\{0.87\right\}$.

Step-by-step solution

Step 1. Given information.

Consider the given question,

$$\begin{gathered} 2\sin x+3\cos x=4x, \\ 0\le x\le 2\mathrm{\pi } \end{gathered}$$

We can say,

$$\begin{gathered} y_1=2\sin x+3\cos x \\ {y}_2=4x \end{gathered}$$

Plot the two equations,

Step 2. Plot the equations for the given interval.

Consider the given question,

The interval is$0\le x\le 2\mathrm{\pi }$.

On plotting the equations for the given interval,

From the graph, we can see the point of intersection is $\left(0.87,3.47\right)$.

Then the solution islocalid="1646496103039" $\left\{0.87\right\}$.