Homework Soursesin225 using half angle identitySolutionBy the halfangle for
sin22.5 using half angle identity
Solution
By the half-angle formula, we have that:
sin(x/2) = ±[(1 - cos x)/2].
We pick the positive sign as sin(22.5°) > 0 as 22.5° is in Quadrant I.
With x = 45°:
sin(45°/2) = [(1 - cos 45°)/2]
==> sin(22.5°) = [(1 - 2/2)/2] = [(2 - 2)/4] = (2 - 2)/2.
=0.38268343
![sin22.5 using half angle identitySolutionBy the half-angle formula, we have that: sin(x/2) = ±[(1 - cos x)/2]. We pick the positive sign as sin(22.5°) > 0 as](/WebImages/3/sin225-using-half-angle-identitysolutionby-the-halfangle-for-972586-1761499770-0.webp "sin22.5 using half angle identitySolutionBy the half-angle formula, we have that: sin(x/2) = ±[(1 - cos x)/2]. We pick the positive sign as sin(22.5°) > 0 as")
