What is the general solution for 6cos(θ)+3=0 ?

The general solution for 6cos(θ)+3=0 is θ=(2pi)/3+2pin,θ=(4pi)/3+2pin

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6cos(θ)+3=0

6 cos (θ) + 3 = 0

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

6 cos (θ) + 3 = 0

Move

3

to the right side

6 cos (θ) + 3 = 0

Subtract

3

from both sides

6 cos (θ) + 3 - 3 = 0 - 3

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}

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{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} (x) + 5 sin (x) + 6 = 0

- 6 tan^{2} (θ) + 11 tan (θ) - 6 = - 2 tan (θ)

(sin (x) + 1)^{2} + cos^{2} (x) = 2

12 sin^{2} (x) - cos (x) - 6 = 0

tan (\frac{x}{2}) - 1 = 0

What is the general solution for 6cos(θ)+3=0 ?
The general solution for 6cos(θ)+3=0 is θ=(2pi)/3+2pin,θ=(4pi)/3+2pin