What is the general solution for 4-4cos(θ)=6 ?

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

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4-4cos(θ)=6

4 - 4 cos (θ) = 6

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

Degrees

θ = 12 0^{\circ} + 36 0^{\circ} n, θ = 24 0^{\circ} + 36 0^{\circ} n

Solution steps

4 - 4 cos (θ) = 6

Move

4

to the right side

4 - 4 cos (θ) = 6

Subtract

4

from both sides

4 - 4 cos (θ) - 4 = 6 - 4

Simplify

- 4 cos (θ) = 2

- 4 cos (θ) = 2

Divide both sides by

- 4

- 4 cos (θ) = 2

Divide both sides by

- 4

\frac{- 4 cos ( θ )}{- 4} = \frac{2}{- 4}

Simplify

\frac{- 4 cos ( θ )}{- 4} = \frac{2}{- 4}

Simplify

\frac{- 4 cos ( θ )}{- 4} : cos (θ)

\frac{- 4 cos ( θ )}{- 4}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{4 cos ( θ )}{4}

Divide the numbers:

\frac{4}{4} = 1

= cos (θ)

Simplify

\frac{2}{- 4} : - \frac{1}{2}

\frac{2}{- 4}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{2}{4}

Cancel the common factor:

2

= - \frac{1}{2}

cos (θ) = - \frac{1}{2}

cos (θ) = - \frac{1}{2}

cos (θ) = - \frac{1}{2}

General solutions for

cos (θ) = - \frac{1}{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{2 π}{3} + 2 πn, θ = \frac{4 π}{3} + 2 πn

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

sin^{2} (θ) - 2 sin (θ) + 1 = 0

cos (4 θ) = - \frac{1}{2}

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

(2 cos (x) - 1) (sin (x) - 1) = 0

cos (3 2^{\circ}) = sin (5 m) - 12

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