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

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

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cos(θ)=0.5

cos (θ) = 0.5

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

Degrees

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

Solution steps

cos (θ) = 0.5

General solutions for

cos (θ) = 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}

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

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

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

cos (\frac{θ}{2}) - 1 = 0

2 sin (5 x) + 3 = 0

cot^{2} (x) + 2 csc (x) = - 1

3 cos (θ) - 1 = 0

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