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

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

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2cos(3x)=-1

2 cos (3 x) = - 1

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

Solution steps

2 cos (3 x) = - 1

Divide both sides by

2

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

General solutions for

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

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

Solve

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

Solve

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

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

6 sin (\frac{θ}{2}) = - 6 cos (\frac{θ}{2})

csc (θ) = - \frac{4}{3}

9 sin^{2} (θ) + 3 cos (θ) - 9 = - 2

2 cos (3 t) - 1 = 0

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

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