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

The general solution for 1/2 =cos(θ) is θ= pi/3+2pin,θ=(5pi)/3+2pin

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1/2 =cos(θ)

\frac{1}{2} = cos (θ)

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

\frac{1}{2} = cos (θ)

Switch sides

cos (θ) = \frac{1}{2}

General solutions for

cos (θ) = \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}

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

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

sin (2 x) cos (x) - sin (x) = 0

9 sec^{2} (x) - 12 = 0

tan^{2} (x) - 7 tan (x) - 8 = 0

5 tan (x) sin (x) = - 7 sin (x)

What is the general solution for 1/2 =cos(θ) ?
The general solution for 1/2 =cos(θ) is θ= pi/3+2pin,θ=(5pi)/3+2pin