Chapter 13.1, Problem 2CYU

To determine

To find : the value of cos $\theta$ .

Answer to Problem 2CYU

  $\cos \theta =\frac{3}{5}$

Explanation of Solution

Given information :

We know that, $\sin \theta =\frac{4}{5},0°<\theta <90°$

Calculation :

  $\begin{array}{l}{\sin }^2\theta +{\cos }^2\theta =1\\ \Rightarrow {\left(\frac{4}{5}\right)}^2+{\cos }^2\theta =1\\ \Rightarrow {\cos }^2\theta =1-\frac{16}{25}=\frac{9}{25}\\ \Rightarrow {\cos }^2\theta =\frac{9}{25}\\ \Rightarrow \cos \theta =\pm \frac{3}{5}\\ \text{But }\theta \text{lies between 0° and 90°}\\ \Rightarrow \cos \theta =\frac{3}{5}\end{array}$