What is the general solution for 2cos(3x-1)=-1 ?

The general solution for 2cos(3x-1)=-1 is x= 1/3+(2pi)/9+(2pin)/3 ,x= 1/3+(4pi)/9+(2pin)/3

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2cos(3x-1)=-1

2 cos (3 x - 1) = - 1

x = \frac{1}{3} + \frac{2 π}{9} + \frac{2 πn}{3}, x = \frac{1}{3} + \frac{4 π}{9} + \frac{2 πn}{3}

Solution steps

2 cos (3 x - 1) = - 1

Divide both sides by

2

cos (3 x - 1) = - \frac{1}{2}

General solutions for

cos (3 x - 1) = - \frac{1}{2}

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

Solve

3 x - 1 = \frac{2 π}{3} + 2 πn : x = \frac{1}{3} + \frac{2 π}{9} + \frac{2 πn}{3}

Solve

3 x - 1 = \frac{4 π}{3} + 2 πn : x = \frac{1}{3} + \frac{4 π}{9} + \frac{2 πn}{3}

x = \frac{1}{3} + \frac{2 π}{9} + \frac{2 πn}{3}, x = \frac{1}{3} + \frac{4 π}{9} + \frac{2 πn}{3}

\frac{0.866}{sin ( x )} = 1.53

3 sin (2 x) + 1 = 2

2 cos^{4} (x) - 2 cos^{2} (x) = 4 cos^{2} (x) - 1

x, t^{2} = 2 sec (x)

(8 cos (x) - 4) (sin (x)) = 0, 0 \leq x < 2 π

What is the general solution for 2cos(3x-1)=-1 ?
The general solution for 2cos(3x-1)=-1 is x= 1/3+(2pi)/9+(2pin)/3 ,x= 1/3+(4pi)/9+(2pin)/3