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

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

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cos(x/2)=1

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

x = 4 πn

Degrees

x = 0^{\circ} + 72 0^{\circ} n

Solution steps

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

General solutions for

cos (\frac{x}{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{x}{2} = 0 + 2 πn

\frac{x}{2} = 0 + 2 πn

Solve

\frac{x}{2} = 0 + 2 πn : x = 4 πn

\frac{x}{2} = 0 + 2 πn

0 + 2 πn = 2 πn

\frac{x}{2} = 2 πn

Multiply both sides by

2

\frac{x}{2} = 2 πn

Multiply both sides by

2

\frac{2 x}{2} = 2 \cdot 2 πn

Simplify

x = 4 πn

x = 4 πn

x = 4 πn

8 sin (x) = 4

tan (\frac{x}{2}) = - 3

11 sin (θ) + 2 = 4 sin (θ) + 2

sec^{2} (x) - tan (x) = 1

cos (θ) = \frac{11}{130}

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