What is the general solution for 3cos(6x)=2 ?

The general solution for 3cos(6x)=2 is x=(0.84106…)/6+(pin)/3 ,x= pi/3-(0.84106…)/6+(pin)/3

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3cos(6x)=2

3 cos (6 x) = 2

x = \frac{0.84106 \dots}{6} + \frac{πn}{3}, x = \frac{π}{3} - \frac{0.84106 \dots}{6} + \frac{πn}{3}

Solution steps

3 cos (6 x) = 2

Divide both sides by

3

cos (6 x) = \frac{2}{3}

Apply trig inverse properties

6 x = arccos (\frac{2}{3}) + 2 πn, 6 x = 2 π - arccos (\frac{2}{3}) + 2 πn

Solve

6 x = arccos (\frac{2}{3}) + 2 πn : x = \frac{arccos ( \frac{2}{3} )}{6} + \frac{πn}{3}

Solve

6 x = 2 π - arccos (\frac{2}{3}) + 2 πn : x = \frac{π}{3} - \frac{arccos ( \frac{2}{3} )}{6} + \frac{πn}{3}

x = \frac{arccos ( \frac{2}{3} )}{6} + \frac{πn}{3}, x = \frac{π}{3} - \frac{arccos ( \frac{2}{3} )}{6} + \frac{πn}{3}

Show solutions in decimal form

x = \frac{0.84106 \dots}{6} + \frac{πn}{3}, x = \frac{π}{3} - \frac{0.84106 \dots}{6} + \frac{πn}{3}

2 cos (t) = 1 + sin (t)

cos (θ) = - \frac{5}{6}, csc (θ)

sin^{2} (x) = - 2 + 3 sin (x) + cos^{2} (x)

sin (x) - 3 cos (x) = - 1

sin (θ) = \frac{- 1}{17}

What is the general solution for 3cos(6x)=2 ?
The general solution for 3cos(6x)=2 is x=(0.84106…)/6+(pin)/3 ,x= pi/3-(0.84106…)/6+(pin)/3