What is the general solution for 4cos(x)=-2 ?

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

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4cos(x)=-2

4 cos (x) = - 2

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

Degrees

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

Solution steps

4 cos (x) = - 2

Divide both sides by

4

4 cos (x) = - 2

Divide both sides by

4

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

Simplify

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

Simplify

\frac{4 cos ( x )}{4} : cos (x)

\frac{4 cos ( x )}{4}

Divide the numbers:

\frac{4}{4} = 1

= cos (x)

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

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

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

General solutions for

cos (x) = - \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}

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

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

3 cos^{2} (x) + cos (x) - 4 = 0

sin (θ) = 7

sin (3 x - \frac{π}{2}) = - \frac{3}{2}, (3 π, 4 π)

2 sin^{2} (x) - 7 cos (x) - 5 = 0

cos (x) = sin (0)

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