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

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

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cos(3θ)=-1/2

cos (3 θ) = - \frac{1}{2}

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

Solution steps

cos (3 θ) = - \frac{1}{2}

General solutions for

cos (3 θ) = - \frac{1}{2}

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

Solve

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

Solve

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

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

cos (x) = \frac{5}{6}

1 - tan^{2} (x) = 0

cos (x) cos (3 x) - sin (x) sin (3 x) = 0

(cot (θ) - 1) (sin (θ) - 1) = 0

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

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