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

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

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-1/2 =cos(x)

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

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

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

Switch sides

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

cos (θ) = - \frac{2}{3}

8 tan (x) sin (x) = 7 sin (x)

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

sin^{3} (x) + cos^{3} (x) = 0

- sin (3 x) \cdot 3 = 0

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