Chapter 13.2, Problem 1WE

To determine

To find: The value number $x$ if $0\le x\le \frac{\pi }{2}$.

Answer to Problem 1WE

The value of $x$ is $\frac{\pi }{3}$ .

Explanation of Solution

Given information:

The given information is $\sin x=\frac{\sqrt{3}}{2}$ .

Calculation:

Table

$\theta$	$\sin \theta$	$\cos \theta$	$\tan \theta$	$\cos ec\theta$	$\sec \theta$	$\cot \theta$
${30}^{\circ }$	$\frac{1}{2}$	$\frac{\sqrt{3}}{2}$	$\frac{\sqrt{3}}{2}$	$2$	$\frac{2\sqrt{3}}{3}$	$\sqrt{3}$
${45}^{\circ }$	$\frac{\sqrt{2}}{2}$	$\frac{\sqrt{2}}{2}$	$1$	$\sqrt{2}$	$\sqrt{2}$	$1$
${60}^{\circ }$	$\frac{\sqrt{3}}{2}$	$\frac{1}{2}$	$\sqrt{3}$	$\frac{2\sqrt{3}}{3}$	$2$	$\frac{\sqrt{3}}{2}$

By using the above table

  $\sin x=\frac{\sqrt{3}}{2}$

  $\begin{array}{c}\sin x=\frac{\sqrt{3}}{2}\\ ={\sin }^{-1}\frac{\sqrt{3}}{2}\\ ={60}^{\circ }\end{array}$

Convert it into radian multiplies by $\frac{\pi }{{180}^{\circ }}$ .

  $\begin{array}{l}x=\frac{\pi }{{180}^{\circ }}\times {60}^{\circ }\\ x=\frac{\pi }{3}\end{array}$

Therefore, the value of $x$ is $\frac{\pi }{3}$ .