Question

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

Answer 1

The answer is ⇒ sinФ/2 = 0.612

Explanation:

∵ cosФ = 1/4

∴ Ф = cos^-1 1/4 = 83.91°

∴ Ф/2 = 83.91 ÷ 2 = 41.96°

∴ sinФ/2 = 0.612

Answer 2

`\sin((\theta)/(2) )=(√(6))/(4)`

Explanation:

Recall and apply the following formula;

`\sin((\theta)/(2) )=\pm \sqrt{(1-\cos(\theta))/(2) }`

Since
`\theta` is acute,

`\sin((\theta)/(2) )=\sqrt{(1-\cos(\theta))/(2) }`

Given
`\cos(\theta)=(1)/(4)`, then

`\sin((\theta)/(2) )=\sqrt{(1-(1)/(4))/(2) }`

`\sin((\theta)/(2) )=(√(6))/(4)`