What is the general solution for 8cos(3x)=2 ?

The general solution for 8cos(3x)=2 is x=(1.31811…)/3+(2pin)/3 ,x=(2pi)/3-(1.31811…)/3+(2pin)/3

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8cos(3x)=2

8 cos (3 x) = 2

x = \frac{1.31811 \dots}{3} + \frac{2 πn}{3}, x = \frac{2 π}{3} - \frac{1.31811 \dots}{3} + \frac{2 πn}{3}

Solution steps

8 cos (3 x) = 2

Divide both sides by

8

cos (3 x) = \frac{1}{4}

Apply trig inverse properties

3 x = arccos (\frac{1}{4}) + 2 πn, 3 x = 2 π - arccos (\frac{1}{4}) + 2 πn

Solve

3 x = arccos (\frac{1}{4}) + 2 πn : x = \frac{arccos ( \frac{1}{4} )}{3} + \frac{2 πn}{3}

Solve

3 x = 2 π - arccos (\frac{1}{4}) + 2 πn : x = \frac{2 π}{3} - \frac{arccos ( \frac{1}{4} )}{3} + \frac{2 πn}{3}

x = \frac{arccos ( \frac{1}{4} )}{3} + \frac{2 πn}{3}, x = \frac{2 π}{3} - \frac{arccos ( \frac{1}{4} )}{3} + \frac{2 πn}{3}

Show solutions in decimal form

x = \frac{1.31811 \dots}{3} + \frac{2 πn}{3}, x = \frac{2 π}{3} - \frac{1.31811 \dots}{3} + \frac{2 πn}{3}

cot^{2} (θ) = 1

tan (\frac{x}{2}) = \frac{4 - π}{π}

sin^{2} (x) = sin^{2} (x) sec (x)

sin (x) - cos (x) = 2

sin (x) = \frac{4.2}{9.5}

What is the general solution for 8cos(3x)=2 ?
The general solution for 8cos(3x)=2 is x=(1.31811…)/3+(2pin)/3 ,x=(2pi)/3-(1.31811…)/3+(2pin)/3