Question

if angle theta is an acute angle such that cos theta =1/4, find sin theta/2

Answer 1

Answer:

The answer is ⇒ sinФ/2 = 0.612

Step-by-step explanation:

∵ cosФ = 1/4

∴ Ф = cos^-1 1/4 = 83.91°

∴ Ф/2 = 83.91 ÷ 2 = 41.96°

∴ sinФ/2 = 0.612

Answer 2

Answer:

$\sin(\frac{\theta}{2} )=\frac{\sqrt{6}}{4}$

Step-by-step explanation:

Recall and apply the following formula;

$\sin(\frac{\theta}{2} )=\pm \sqrt{\frac{1-\cos(\theta)}{2} }$

Since $\theta$ is acute,

$\sin(\frac{\theta}{2} )=\sqrt{\frac{1-\cos(\theta)}{2} }$

Given $\cos(\theta)=\frac{1}{4}$, then

$\sin(\frac{\theta}{2} )=\sqrt{\frac{1-\frac{1}{4}}{2} }$

$\sin(\frac{\theta}{2} )=\frac{\sqrt{6}}{4}$