A) arcsin(cos 22pi/5) b) sin(arccos(-2/5)

Question

A) arcsin(cos 22pi/5) b) sin(arccos(-2/5)

Answer 1

А)
ArcSin(Cos(22п/5)) = ArcSin(Cos(2п + 2п + 2п/5)) = ArcSin(Cos(2п/5)) = п/2 - ArcCos(Cos(2п/5)) = п/2 - 2п/5 = п/10
Б) Sin(Arccos(-2/5)) = √(1 - Cos²(Arccos(-2/5))) = √(1 - (2/5)²) = (√21)/5