Chapter 14.8, Problem 7OE

To determine

To find:the number of solutions does the given equation have the interval $0\le x\le 2\pi$ .

Answer to Problem 7OE

Onesolution, $x={175.2}^{\circ }{}^{\circ }$ .

Explanation of Solution

Given:

The given equation is $\sin \frac{x}{9}=\frac{1}{3}$ .

Calculation:

As thegiven equation is $\sin \frac{x}{9}=\frac{1}{3}$ .

Now, to find the solutions of the given equation. Therefore,

  $\begin{array}{l}\sin \frac{x}{9}=\frac{1}{3}\{\text{given equation}}\\ \therefore \frac{x}{9}={\sin }^{-1}\left(\frac{1}{3}\right)\{\text{simplify}}\\ \Rightarrow \frac{x}{9}={19.47}^{\circ }\left\{{\sin }^{-1}\left(\frac{1}{3}\right)={19.47}^{\circ }\right\}\\ x={19.47}^{\circ }\times 9\left\{multiplybothsidesby9\right\}\\ x={175.2}^{\circ }\end{array}$

Hence, the solutions have only one solution i.e. $x={175.2}^{\circ }{}^{\circ }$ .