What is the general solution for 3cos(2x)=2 ?

The general solution for 3cos(2x)=2 is x=(0.84106…)/2+pin,x=pi-(0.84106…)/2+pin

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3cos(2x)=2

3 cos (2 x) = 2

x = \frac{0.84106 \dots}{2} + πn, x = π - \frac{0.84106 \dots}{2} + πn

Degrees

x = 24.09484 \dots^{\circ} + 18 0^{\circ} n, x = 155.90515 \dots^{\circ} + 18 0^{\circ} n

Solution steps

3 cos (2 x) = 2

Divide both sides by

3

3 cos (2 x) = 2

Divide both sides by

3

\frac{3 cos ( 2 x )}{3} = \frac{2}{3}

Simplify

cos (2 x) = \frac{2}{3}

cos (2 x) = \frac{2}{3}

Apply trig inverse properties

cos (2 x) = \frac{2}{3}

General solutions for

cos (2 x) = \frac{2}{3}

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

2 x = arccos (\frac{2}{3}) + 2 πn, 2 x = 2 π - arccos (\frac{2}{3}) + 2 πn

2 x = arccos (\frac{2}{3}) + 2 πn, 2 x = 2 π - arccos (\frac{2}{3}) + 2 πn

Solve

2 x = arccos (\frac{2}{3}) + 2 πn : x = \frac{arccos ( \frac{2}{3} )}{2} + πn

2 x = arccos (\frac{2}{3}) + 2 πn

Divide both sides by

2

2 x = arccos (\frac{2}{3}) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{arccos ( \frac{2}{3} )}{2} + \frac{2 πn}{2}

Simplify

x = \frac{arccos ( \frac{2}{3} )}{2} + πn

x = \frac{arccos ( \frac{2}{3} )}{2} + πn

Solve

2 x = 2 π - arccos (\frac{2}{3}) + 2 πn : x = π - \frac{arccos ( \frac{2}{3} )}{2} + πn

2 x = 2 π - arccos (\frac{2}{3}) + 2 πn

Divide both sides by

2

2 x = 2 π - arccos (\frac{2}{3}) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{2 π}{2} - \frac{arccos ( \frac{2}{3} )}{2} + \frac{2 πn}{2}

Simplify

x = π - \frac{arccos ( \frac{2}{3} )}{2} + πn

x = π - \frac{arccos ( \frac{2}{3} )}{2} + πn

x = \frac{arccos ( \frac{2}{3} )}{2} + πn, x = π - \frac{arccos ( \frac{2}{3} )}{2} + πn

Show solutions in decimal form

x = \frac{0.84106 \dots}{2} + πn, x = π - \frac{0.84106 \dots}{2} + πn

3 cos (2 x) = 0

3 cos (x) - 3 sin (x) = 0

sin^{3} (x) = 3 sin (x) - 4 sin^{3} (x)

tan (θ) = \frac{2}{3 + 2 cos ( 4 5 ^{\circ} )}

cos (2 θ) + 6 cos^{2} (θ) = 5

What is the general solution for 3cos(2x)=2 ?
The general solution for 3cos(2x)=2 is x=(0.84106…)/2+pin,x=pi-(0.84106…)/2+pin