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

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

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3cos(3x)=2

3 cos (3 x) = 2

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

Solution steps

3 cos (3 x) = 2

Divide both sides by

3

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

Apply trig inverse properties

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}

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}

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}

sec (θ) - 2 = - tan (θ) - 3

sin^{2} (x) - sin (x) = 1

2 sin (x) cos (x) + 1 sin (x) = 0

cos (y) = \frac{1}{2}

tan (x) = \frac{cos ( x )}{sin ( x )}

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