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

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

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cos(3x)= 2/3

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

x = \frac{0.84106 \dots}{3} + \frac{2 πn}{3}, x = \frac{2 π}{3} - \frac{0.84106 \dots}{3} + \frac{2 πn}{3}

Degrees

x = 16.06322 \dots^{\circ} + 12 0^{\circ} n, x = 103.93677 \dots^{\circ} + 12 0^{\circ} n

Solution steps

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

Apply trig inverse properties

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

General solutions for

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

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

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

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

Solve

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

3 x = arccos (\frac{2}{3}) + 2 πn

Divide both sides by

3

3 x = arccos (\frac{2}{3}) + 2 πn

Divide both sides by

3

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

Simplify

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

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

Solve

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

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

Divide both sides by

3

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

Divide both sides by

3

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

Simplify

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

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

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

Show solutions in decimal form

x = \frac{0.84106 \dots}{3} + \frac{2 πn}{3}, x = \frac{2 π}{3} - \frac{0.84106 \dots}{3} + \frac{2 πn}{3}

cos (x) (csc (x) + 2) = 0

arctan (θ) = \frac{π}{4}

4 cos^{3} (x) - 7 cos (x) - 3 = 0

\frac{sin ( θ )}{1.3} = \frac{sin ( 12 5 ^{\circ} )}{2.8519}

cot^{2} (θ) = \frac{1}{3}

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