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

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

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cos(a)=-1/2

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

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

Degrees

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

Solution steps

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

General solutions for

cos (a) = - \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}

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

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

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

sin^{2} (θ) = 2 cos (θ) + 2

cos (4 x) (cos (x) - 1) = 0

3 tan (\frac{x}{2}) + 3 = 0

4 cos (x) tan (x) = 5 tan (x)

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