Answer:
Option B [tex]\frac{24}{25}[/tex]
Step-by-step explanation:
we know that
[tex]sin(2\theta) = 2 sin(\theta) cos(\theta)[/tex]
In this problem we have
[tex]cos(\theta)=\frac{4}{5}[/tex]
Find the value of [tex]sin(\theta)[/tex]
Remember that
[tex]sin^{2} (\theta)+cos^{2} (\theta)=1[/tex]
substitute the value
[tex]sin^{2} (\theta)+(\frac{4}{5})^{2}=1[/tex]
[tex]sin^{2} (\theta)=1-\frac{16}{25}[/tex]
[tex]sin^{2} (\theta)=\frac{9}{25}[/tex]
[tex]sin(\theta)=\frac{3}{5}[/tex]
Find the value of [tex]sin(2\theta)[/tex]
[tex]sin(2\theta) = 2 (\frac{3}{5})(\frac{4}{5})[/tex]
[tex]sin(2\theta) = \frac{24}{25}[/tex]
