Chapter 14.1, Problem 3CYU

To determine

To find :The value of sin $\theta$ .

Answer to Problem 3CYU

  $\sin \theta =\frac{\sqrt{5}}{3}$

Explanation of Solution

Given information :

We know that, $\cos \theta =\frac{2}{3},0°<\theta <90°$

Calculation :

  $\begin{array}{l}{\sin }^2\theta +{\cos }^2\theta =1\\ \Rightarrow {\sin }^2\theta +{\left(\frac{2}{3}\right)}^2=1\\ \Rightarrow {\sin }^2\theta =1-\frac{4}{9}=\frac{5}{9}\\ \Rightarrow \sin \theta =\pm \frac{\sqrt{5}}{3}\\ \text{But }0°<\theta <90°\\ \Rightarrow \sin \theta =\frac{\sqrt{5}}{3}\end{array}$