given that sin(theta)=0.3806 and theta is in quadrant I, find sin theta/2

Question

The answer should be rounded to four decimal places as needed

Answer 1

sinθ = 0.3806

 

θ = sin^-1(0.3806) = 22.371º (in quadrant I)

 

sin(θ/2) = sin(22.371º / 2) = 0.19399

Answer 2

Let x=theta

 

sinx = 0.3806

 

 

Use the half-angle formula.

 

sin(x/2) = √[(1 - cosx) / 2]

 

 

But first, you need to find cosx, which is easily found using the Pythagorean theorem identity

 

cosx = √(1 - sin²x)

 

 

Plugging in sinx into this identity,

 

cosx = √[(1 - (0.3806)²]

 

 

Once you have your cosx value, plug it into the half-angle formula.