What is the general solution for -4-6cos(θ)=-7 ?

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

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-4-6cos(θ)=-7

- 4 - 6 cos (θ) = - 7

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

Degrees

θ = 6 0^{\circ} + 36 0^{\circ} n, θ = 30 0^{\circ} + 36 0^{\circ} n

Solution steps

- 4 - 6 cos (θ) = - 7

Move

4

to the right side

- 4 - 6 cos (θ) = - 7

Add

4

to both sides

- 4 - 6 cos (θ) + 4 = - 7 + 4

Simplify

- 6 cos (θ) = - 3

- 6 cos (θ) = - 3

Divide both sides by

- 6

- 6 cos (θ) = - 3

Divide both sides by

- 6

\frac{- 6 cos ( θ )}{- 6} = \frac{- 3}{- 6}

Simplify

\frac{- 6 cos ( θ )}{- 6} = \frac{- 3}{- 6}

Simplify

\frac{- 6 cos ( θ )}{- 6} : cos (θ)

\frac{- 6 cos ( θ )}{- 6}

Apply the fraction rule:

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

= \frac{6 cos ( θ )}{6}

Divide the numbers:

\frac{6}{6} = 1

= cos (θ)

Simplify

\frac{- 3}{- 6} : \frac{1}{2}

\frac{- 3}{- 6}

Apply the fraction rule:

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

= \frac{3}{6}

Cancel the common factor:

3

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

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

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