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.

$\sin \left(x\right)=\ln \left(x\right)$

Short answer

The solution set is $\left\{2.22\right\}$.

Step-by-step solution

Step 1. Given information.

Consider the given question,

$$\begin{gathered} \sin \left(x\right)=\ln \left(x\right), \\ 0\le x\le 2\mathrm{\pi } \end{gathered}$$

We can say,

$$\begin{gathered} y_1=\sin \left(x\right) \\ {y}_2=\ln \left(x\right) \end{gathered}$$

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 $\left(2.22,0.8\right)$.

Then the solution is$\left\{2.22\right\}$.