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

The general solution for 2cos(3θ)=2 is θ=(2pin)/3

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2cos(3θ)=2

2 cos (3 θ) = 2

θ = \frac{2 πn}{3}

Degrees

θ = 0^{\circ} + 12 0^{\circ} n

Solution steps

2 cos (3 θ) = 2

Divide both sides by

2

2 cos (3 θ) = 2

Divide both sides by

2

\frac{2 cos ( 3 θ )}{2} = \frac{2}{2}

Simplify

cos (3 θ) = 1

cos (3 θ) = 1

General solutions for

cos (3 θ) = 1

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

3 θ = 0 + 2 πn

3 θ = 0 + 2 πn

Solve

3 θ = 0 + 2 πn : θ = \frac{2 πn}{3}

3 θ = 0 + 2 πn

0 + 2 πn = 2 πn

3 θ = 2 πn

Divide both sides by

3

3 θ = 2 πn

Divide both sides by

3

\frac{3 θ}{3} = \frac{2 πn}{3}

Simplify

θ = \frac{2 πn}{3}

θ = \frac{2 πn}{3}

θ = \frac{2 πn}{3}

tan (θ) = 2, 0 < θ < (\frac{π}{2}), sin (\frac{θ}{2})

sinh (a) = \frac{1}{2}

sin (x) = \frac{- 1}{\frac{5}{2}}

2 csc^{2} (θ) - 3 cot (θ) + 3 = 0

\frac{2 sin ( x ) + 1}{cos ( x )} = 0

What is the general solution for 2cos(3θ)=2 ?
The general solution for 2cos(3θ)=2 is θ=(2pin)/3