What is the general solution for -2cos(x)=1 ?

The general solution for -2cos(x)=1 is x=(2pi)/3+2pin,x=(4pi)/3+2pin

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-2cos(x)=1

- 2 cos (x) = 1

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

- 2 cos (x) = 1

Divide both sides by

- 2

- 2 cos (x) = 1

Divide both sides by

- 2

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

Simplify

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

0 = 6 cos (3 t)

2 cos (x) = sin (x) + 1

cos (z) = \frac{5}{4}

cos (B) = \frac{3}{8}

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

What is the general solution for -2cos(x)=1 ?
The general solution for -2cos(x)=1 is x=(2pi)/3+2pin,x=(4pi)/3+2pin