What is the general solution for cos(a)=0.5 ?

The general solution for cos(a)=0.5 is a= pi/3+2pin,a=(5pi)/3+2pin

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cos(a)=0.5

cos (a) = 0.5

a = \frac{π}{3} + 2 πn, a = \frac{5 π}{3} + 2 πn

Degrees

a = 6 0^{\circ} + 36 0^{\circ} n, a = 30 0^{\circ} + 36 0^{\circ} n

Solution steps

cos (a) = 0.5

General solutions for

cos (a) = 0.5

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{π}{3} + 2 πn, a = \frac{5 π}{3} + 2 πn

a = \frac{π}{3} + 2 πn, a = \frac{5 π}{3} + 2 πn

2 cos^{2} (θ) - 3 cos (θ) - 2 = 0

- 7 sin^{2} (θ) + 4 sin (θ) = - 3

3 = 3 cos (2 x) + sin (2 x)

csc (θ) = - \frac{2 3}{3}

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

What is the general solution for cos(a)=0.5 ?
The general solution for cos(a)=0.5 is a= pi/3+2pin,a=(5pi)/3+2pin