What is the general solution for 4cos(3θ)=2 ?

The general solution for 4cos(3θ)=2 is θ= pi/9+(2pin)/3 ,θ=(5pi)/9+(2pin)/3

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4cos(3θ)=2

4 cos (3 θ) = 2

θ = \frac{π}{9} + \frac{2 πn}{3}, θ = \frac{5 π}{9} + \frac{2 πn}{3}

Solution steps

4 cos (3 θ) = 2

Divide both sides by

4

cos (3 θ) = \frac{1}{2}

General solutions for

cos (3 θ) = \frac{1}{2}

3 θ = \frac{π}{3} + 2 πn, 3 θ = \frac{5 π}{3} + 2 πn

Solve

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

Solve

3 θ = \frac{5 π}{3} + 2 πn : θ = \frac{5 π}{9} + \frac{2 πn}{3}

θ = \frac{π}{9} + \frac{2 πn}{3}, θ = \frac{5 π}{9} + \frac{2 πn}{3}

sin (x) = - 0.8176

sin (x) = - 0.342

(cos (x) - 4) (cos (x) + 1) = 0

- 15 + 4 cos (x) = - 15 - 22

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

What is the general solution for 4cos(3θ)=2 ?
The general solution for 4cos(3θ)=2 is θ= pi/9+(2pin)/3 ,θ=(5pi)/9+(2pin)/3