What is the general solution for cos(2x)-0.25=0 ?

The general solution for cos(2x)-0.25=0 is x=(1.31811…)/2+pin,x=pi-(1.31811…)/2+pin

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cos(2x)-0.25=0

cos (2 x) - 0.25 = 0

x = \frac{1.31811 \dots}{2} + πn, x = π - \frac{1.31811 \dots}{2} + πn

Degrees

x = 37.76124 \dots^{\circ} + 18 0^{\circ} n, x = 142.23875 \dots^{\circ} + 18 0^{\circ} n

Solution steps

cos (2 x) - 0.25 = 0

Move

0.25

to the right side

cos (2 x) - 0.25 = 0

Add

0.25

to both sides

cos (2 x) - 0.25 + 0.25 = 0 + 0.25

Simplify

cos (2 x) = 0.25

cos (2 x) = 0.25

Apply trig inverse properties

cos (2 x) = 0.25

General solutions for

cos (2 x) = 0.25

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

2 x = arccos (0.25) + 2 πn, 2 x = 2 π - arccos (0.25) + 2 πn

2 x = arccos (0.25) + 2 πn, 2 x = 2 π - arccos (0.25) + 2 πn

Solve

2 x = arccos (0.25) + 2 πn : x = \frac{arccos ( 0.25 )}{2} + πn

2 x = arccos (0.25) + 2 πn

Divide both sides by

2

2 x = arccos (0.25) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{arccos ( 0.25 )}{2} + \frac{2 πn}{2}

Simplify

x = \frac{arccos ( 0.25 )}{2} + πn

x = \frac{arccos ( 0.25 )}{2} + πn

Solve

2 x = 2 π - arccos (0.25) + 2 πn : x = π - \frac{arccos ( 0.25 )}{2} + πn

2 x = 2 π - arccos (0.25) + 2 πn

Divide both sides by

2

2 x = 2 π - arccos (0.25) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{2 π}{2} - \frac{arccos ( 0.25 )}{2} + \frac{2 πn}{2}

Simplify

x = π - \frac{arccos ( 0.25 )}{2} + πn

x = π - \frac{arccos ( 0.25 )}{2} + πn

x = \frac{arccos ( 0.25 )}{2} + πn, x = π - \frac{arccos ( 0.25 )}{2} + πn

Show solutions in decimal form

x = \frac{1.31811 \dots}{2} + πn, x = π - \frac{1.31811 \dots}{2} + πn

What is the general solution for cos(2x)-0.25=0 ?
The general solution for cos(2x)-0.25=0 is x=(1.31811…)/2+pin,x=pi-(1.31811…)/2+pin