From the given image,
[tex]\cos(\theta)=\frac{9}{41}[/tex]
Recall the trigonometric identity:
[tex]\sin^2(\frac{\theta}{2})=\frac{1-\cos(\theta)}{2}[/tex]
Substitute cos (θ) = 9/41 into the equation:
[tex]\sin^2(\frac{\theta}{2})=\frac{1-\frac{9}{41}}{2}=\frac{41-9}{82}=\frac{32}{82}=\frac{16}{41}[/tex]
Therefore,
[tex]\sin(\frac{\theta}{2})=\sqrt{\frac{16}{41}}=\frac{4\sqrt{41}}{41}[/tex]
Therefore, the required answer is:
sin(θ/2) = (4√41)/41
.
