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

The general solution for cos(θ/2)=1 is θ=4pin

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cos(θ/2)=1

cos (\frac{θ}{2}) = 1

θ = 4 πn

Degrees

θ = 0^{\circ} + 72 0^{\circ} n

Solution steps

cos (\frac{θ}{2}) = 1

General solutions for

cos (\frac{θ}{2}) = 1

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}

\frac{θ}{2} = 0 + 2 πn

\frac{θ}{2} = 0 + 2 πn

Solve

\frac{θ}{2} = 0 + 2 πn : θ = 4 πn

\frac{θ}{2} = 0 + 2 πn

0 + 2 πn = 2 πn

\frac{θ}{2} = 2 πn

Multiply both sides by

2

\frac{θ}{2} = 2 πn

Multiply both sides by

2

\frac{2 θ}{2} = 2 \cdot 2 πn

Simplify

θ = 4 πn

θ = 4 πn

θ = 4 πn

csc^{2} (θ) + csc (θ) - 2 = 0

2 sin (x) = cos (x)

2 + 2 sin (θ) = 4 cos^{2} (θ)

9 tan (x) sin (x) - 5 sin (x) = 0

x, y = arctan (x)

What is the general solution for cos(θ/2)=1 ?
The general solution for cos(θ/2)=1 is θ=4pin