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

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

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cos(2x)=0.25

cos (2 x) = 0.25

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

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

3 cos^{2} (x) = 2

3 tan (θ) = 2 sin (θ)

sin (x) = - 0.1

189.4 = 100 tan^{2} (4 5^{\circ} + \frac{θ}{2})

csc (θ) = 1 + cot (θ)

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