What is the general solution for cos(2x)=0.2 ?

The general solution for cos(2x)=0.2 is x=(1.36943…)/2+pin,x=pi-(1.36943…)/2+pin

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cos(2x)=0.2

cos (2 x) = 0.2

x = \frac{1.36943 \dots}{2} + πn, x = π - \frac{1.36943 \dots}{2} + πn

Degrees

x = 39.23152 \dots^{\circ} + 18 0^{\circ} n, x = 140.76847 \dots^{\circ} + 18 0^{\circ} n

Solution steps

cos (2 x) = 0.2

Apply trig inverse properties

cos (2 x) = 0.2

General solutions for

cos (2 x) = 0.2

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

2 x = arccos (0.2) + 2 πn, 2 x = 2 π - arccos (0.2) + 2 πn

2 x = arccos (0.2) + 2 πn, 2 x = 2 π - arccos (0.2) + 2 πn

Solve

2 x = arccos (0.2) + 2 πn : x = \frac{arccos ( 0.2 )}{2} + πn

2 x = arccos (0.2) + 2 πn

Divide both sides by

2

2 x = arccos (0.2) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{arccos ( 0.2 )}{2} + \frac{2 πn}{2}

Simplify

x = \frac{arccos ( 0.2 )}{2} + πn

x = \frac{arccos ( 0.2 )}{2} + πn

Solve

2 x = 2 π - arccos (0.2) + 2 πn : x = π - \frac{arccos ( 0.2 )}{2} + πn

2 x = 2 π - arccos (0.2) + 2 πn

Divide both sides by

2

2 x = 2 π - arccos (0.2) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{2 π}{2} - \frac{arccos ( 0.2 )}{2} + \frac{2 πn}{2}

Simplify

x = π - \frac{arccos ( 0.2 )}{2} + πn

x = π - \frac{arccos ( 0.2 )}{2} + πn

x = \frac{arccos ( 0.2 )}{2} + πn, x = π - \frac{arccos ( 0.2 )}{2} + πn

Show solutions in decimal form

x = \frac{1.36943 \dots}{2} + πn, x = π - \frac{1.36943 \dots}{2} + πn

cos (2 x) = 0.6

cos (x) = \frac{- 3}{10}

sin (θ) = \frac{21}{5}

sin (α) = \frac{3}{5}

x, tan^{2} (x) = 1

What is the general solution for cos(2x)=0.2 ?
The general solution for cos(2x)=0.2 is x=(1.36943…)/2+pin,x=pi-(1.36943…)/2+pin