so cos4x = 0 means 4x = π/2+2kπ or 3π/2+2kπ
That simplifies to x = π/8 + kπ/4
or cosx = 1
so x=0
Find all the solutions of the equation in the interval [0, 2π):
cos 4x(cos x - 1) = 0
2 answers
cos 4x(cos x - 1) = 0
cos 4x = 0 or cosx = 1
the easy one first:
cosx = 1 , so x = 0, 2π
cos 4x = 0 ,
so 4x = π/2 or 4x = 3π/2
x = π/8 or x = 3π/8
but the period of cos 4x = 2π/4 = π/2
so other solutions are π/8 + π/2, π/8 + 2π/2, π/8 + 3π/2, π/8 + 4π/2,
and 3π/8 , 5π/8, 7π/8, 9π/8, 11π/8, 13π/8 , 15π/8, 2π rest are outside of domain
x = 0, π/8, 3π/8, 5π/8, 7π/9, 9π/8, 11π/8, 13π/8, 15π/8, 2π
( in degrees: 0, 22.5, 67.5, 112.5. 157.5, 202.5, 247.5, 292.5, 337.5, 360 )
cos 4x = 0 or cosx = 1
the easy one first:
cosx = 1 , so x = 0, 2π
cos 4x = 0 ,
so 4x = π/2 or 4x = 3π/2
x = π/8 or x = 3π/8
but the period of cos 4x = 2π/4 = π/2
so other solutions are π/8 + π/2, π/8 + 2π/2, π/8 + 3π/2, π/8 + 4π/2,
and 3π/8 , 5π/8, 7π/8, 9π/8, 11π/8, 13π/8 , 15π/8, 2π rest are outside of domain
x = 0, π/8, 3π/8, 5π/8, 7π/9, 9π/8, 11π/8, 13π/8, 15π/8, 2π
( in degrees: 0, 22.5, 67.5, 112.5. 157.5, 202.5, 247.5, 292.5, 337.5, 360 )