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

The general solution for 2cos(θ)+2sqrt(3)=sqrt(3) is θ=(5pi)/6+2pin,θ=(7pi)/6+2pin

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2cos(θ)+2sqrt(3)=sqrt(3)

2 cos (θ) + 23 = 3

θ = \frac{5 π}{6} + 2 πn, θ = \frac{7 π}{6} + 2 πn

Degrees

θ = 15 0^{\circ} + 36 0^{\circ} n, θ = 21 0^{\circ} + 36 0^{\circ} n

Solution steps

2 cos (θ) + 23 = 3

Move

23

to the right side

2 cos (θ) + 23 = 3

Subtract

23

from both sides

2 cos (θ) + 23 - 23 = 3 - 23

Simplify

2 cos (θ) + 23 - 23 = 3 - 23

Simplify

2 cos (θ) + 23 - 23 : 2 cos (θ)

2 cos (θ) + 23 - 23

Add similar elements:

23 - 23 = 0

= 2 cos (θ)

Simplify

3 - 23 : - 3

3 - 23

Add similar elements:

3 - 23 = - 3

= - 3

2 cos (θ) = - 3

2 cos (θ) = - 3

2 cos (θ) = - 3

Divide both sides by

2

2 cos (θ) = - 3

Divide both sides by

2

\frac{2 cos ( θ )}{2} = \frac{- 3}{2}

Simplify

cos (θ) = - \frac{3}{2}

cos (θ) = - \frac{3}{2}

General solutions for

cos (θ) = - \frac{3}{2}

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}

θ = \frac{5 π}{6} + 2 πn, θ = \frac{7 π}{6} + 2 πn

θ = \frac{5 π}{6} + 2 πn, θ = \frac{7 π}{6} + 2 πn

What is the general solution for 2cos(θ)+2sqrt(3)=sqrt(3) ?
The general solution for 2cos(θ)+2sqrt(3)=sqrt(3) is θ=(5pi)/6+2pin,θ=(7pi)/6+2pin