What is the general solution for 2cos(θ)+5sqrt(3)=4sqrt(3) ?

The general solution for 2cos(θ)+5sqrt(3)=4sqrt(3) is θ=(5pi)/6+2pin,θ=(7pi)/6+2pin

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2cos(θ)+5sqrt(3)=4sqrt(3)

2 cos (θ) + 53 = 43

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) + 53 = 43

Move

53

to the right side

2 cos (θ) + 53 = 43

Subtract

53

from both sides

2 cos (θ) + 53 - 53 = 43 - 53

Simplify

2 cos (θ) + 53 - 53 = 43 - 53

Simplify

2 cos (θ) + 53 - 53 : 2 cos (θ)

2 cos (θ) + 53 - 53

Add similar elements:

53 - 53 = 0

= 2 cos (θ)

Simplify

43 - 53 : - 3

43 - 53

Add similar elements:

43 - 53 = - 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

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

sin (x) = - cos^{2} (x) - 1, 0 \leq x \leq 2 π

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

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

cos (θ) tan (θ) + cot (θ) = csc (θ)

What is the general solution for 2cos(θ)+5sqrt(3)=4sqrt(3) ?
The general solution for 2cos(θ)+5sqrt(3)=4sqrt(3) is θ=(5pi)/6+2pin,θ=(7pi)/6+2pin