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

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

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cos(2x)=0.4

cos (2 x) = 0.4

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

Degrees

x = 33.21091 \dots^{\circ} + 18 0^{\circ} n, x = 146.78908 \dots^{\circ} + 18 0^{\circ} n

Solution steps

cos (2 x) = 0.4

Apply trig inverse properties

cos (2 x) = 0.4

General solutions for

cos (2 x) = 0.4

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

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

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

Solve

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

2 x = arccos (0.4) + 2 πn

Divide both sides by

2

2 x = arccos (0.4) + 2 πn

Divide both sides by

2

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

Simplify

x = \frac{arccos ( 0.4 )}{2} + πn

x = \frac{arccos ( 0.4 )}{2} + πn

Solve

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

2 x = 2 π - arccos (0.4) + 2 πn

Divide both sides by

2

2 x = 2 π - arccos (0.4) + 2 πn

Divide both sides by

2

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

Simplify

x = π - \frac{arccos ( 0.4 )}{2} + πn

x = π - \frac{arccos ( 0.4 )}{2} + πn

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

Show solutions in decimal form

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

arcsin (x) = \frac{5 π}{6}

2 cos^{2} (t) - cos (t) = 1

- 2 sin (t) + cos (2 t) \cdot 2 = 0

tan (a) = \frac{4}{3}

5 sin (θ) - 1 = 0

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