Chapter 7.5, Problem 17E

To determine

To find: the principal value of x in degrees.

Answer to Problem 17E

  $45°$

Explanation of Solution

Given information:

  $\sqrt{2}\sin x-1=0$

Calculation:

The principal value of x for the given equation as follows:

  $\begin{array}{c}\sqrt{2}\sin x-1=0\end{array}$

  $\begin{array}{c}\sqrt{2}\sin x=1\left[\text{Add 1 on each side}\right]\end{array}$

  $\begin{array}{c}\sin x=\frac{1}{\sqrt{2}}\left[\text{Divide each side by}\sqrt{2}\right]\end{array}$

  $\begin{array}{c}\sin x=\frac{1}{\sqrt{2}}\left(\frac{\sqrt{2}}{\sqrt{2}}\right)\left[\text{Multiply and divide by}\sqrt{2}\right]\end{array}$

  $\begin{array}{c}\sin x=\frac{\sqrt{2}}{2}\end{array}$

  $\begin{array}{c}x=45°\end{array}$

Thus the principal value of x is $45°$ .