What is the general solution for cos(2x-1)=0.4 ?

The general solution for cos(2x-1)=0.4 is x=pin+1/2+(1.15927…)/2 ,x=pi+pin+1/2-(1.15927…)/2

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cos(2x-1)=0.4

cos (2 x - 1) = 0.4

x = πn + \frac{1}{2} + \frac{1.15927 \dots}{2}, x = π + πn + \frac{1}{2} - \frac{1.15927 \dots}{2}

Solution steps

cos (2 x - 1) = 0.4

Apply trig inverse properties

2 x - 1 = arccos (0.4) + 2 πn, 2 x - 1 = 2 π - arccos (0.4) + 2 πn

Solve

2 x - 1 = arccos (0.4) + 2 πn : x = πn + \frac{1}{2} + \frac{arccos ( 0.4 )}{2}

Solve

2 x - 1 = 2 π - arccos (0.4) + 2 πn : x = π + πn + \frac{1}{2} - \frac{arccos ( 0.4 )}{2}

x = πn + \frac{1}{2} + \frac{arccos ( 0.4 )}{2}, x = π + πn + \frac{1}{2} - \frac{arccos ( 0.4 )}{2}

Show solutions in decimal form

x = πn + \frac{1}{2} + \frac{1.15927 \dots}{2}, x = π + πn + \frac{1}{2} - \frac{1.15927 \dots}{2}

cos (3 x) cos (x) = 2 cos (2 x) cos (x)

0 = cos (2 x) - cos (x)

cos (θ) = 0.6015

sin (θ) = \frac{- 4}{5}

θ, x = 5 sec (θ)

What is the general solution for cos(2x-1)=0.4 ?
The general solution for cos(2x-1)=0.4 is x=pin+1/2+(1.15927…)/2 ,x=pi+pin+1/2-(1.15927…)/2