Answer:
[tex]sin(2\theta)=\frac{\sqrt{15}}{8}[/tex]
Step-by-step explanation:
We are given
[tex]sin(\theta)=-\frac{1}{4}[/tex]
Firstly, we can draw triangle
angle lies in third quadrant
so, we get
[tex]cos(\theta)=-\frac{\sqrt{15} }{4}[/tex]
now, we can use formula
[tex]sin(2\theta)=2sin(\theta)\times cos(\theta)[/tex]
now, we can plug values
[tex]sin(2\theta)=2\times -\frac{1}{4}\times -\frac{\sqrt{15} }{4}[/tex]
now, we can simplify it
and we get
[tex]sin(2\theta)=\frac{\sqrt{15}}{8}[/tex]
