Answer:
[tex]\sin(\frac{\theta}{2} )=\frac{\sqrt{6}}{4}[/tex]
Step-by-step explanation:
Recall and apply the following formula;
[tex]\sin(\frac{\theta}{2} )=\pm \sqrt{\frac{1-\cos(\theta)}{2} }[/tex]
Since [tex]\theta[/tex] is acute,
[tex]\sin(\frac{\theta}{2} )=\sqrt{\frac{1-\cos(\theta)}{2} }[/tex]
Given [tex]\cos(\theta)=\frac{1}{4}[/tex], then
[tex]\sin(\frac{\theta}{2} )=\sqrt{\frac{1-\frac{1}{4}}{2} }[/tex]
[tex]\sin(\frac{\theta}{2} )=\frac{\sqrt{6}}{4}[/tex]
