cos (9/8 pi) = ???

Question

Please help me. No calculators allowed. I think we are supposed to use the half angle formula

Answer 1

Cos (9π/8) = Cos ( π + π/8) = -Cos π/8

Cos 2x = Cos² x - Sin²x
Cos 2x = Cos² x - (1 - Cos²x)
Cos 2x = 2Cos² x - 1
Cos² x = (Cos 2x + 1)/2
Cos² π/8 = [ cos π/4 + 1 ] /2
Cos² π/8 = (1/√2 + 1)/2
Cos π/8 = √(1/2√2 + 1/2)

but - Cos π/8 = Cos 9π/8

so Cos 9π/8 = -√(1/2√2 + 1/2)

Answer 2

hi

clarifying

cos (9/8 pi ) = cos (pi + pi/8) = - cos(pi/8)

cos (pi/8) =
= root[ (1+ cos(pi/4)) / 2]
= root[ (1+ root(2)/2) / 2]
= root[ (2+ root(2) / 4]
= {root[(2+ root(2)]} / 2


bye

Answer 3

cos(9/8pi) =cos(pi-1/2pi/4) = -cos(1/2pi/4) =-sqrt((1+2^1/2/2)/2))
as cos pi/4 =2^1/2/2