What is the general solution for 0=1+cos(x/2) ?

The general solution for 0=1+cos(x/2) is x=2pi+4pin

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0=1+cos(x/2)

0 = 1 + cos (\frac{x}{2})

x = 2 π + 4 πn

Degrees

x = 36 0^{\circ} + 72 0^{\circ} n

Solution steps

0 = 1 + cos (\frac{x}{2})

Switch sides

1 + cos (\frac{x}{2}) = 0

Move

1

to the right side

1 + cos (\frac{x}{2}) = 0

Subtract

1

from both sides

1 + cos (\frac{x}{2}) - 1 = 0 - 1

Simplify

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

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} = π + 2 πn

\frac{x}{2} = π + 2 πn

Solve

\frac{x}{2} = π + 2 πn : x = 2 π + 4 πn

\frac{x}{2} = π + 2 πn

Multiply both sides by

2

\frac{x}{2} = π + 2 πn

Multiply both sides by

2

\frac{2 x}{2} = 2 π + 2 \cdot 2 πn

Simplify

x = 2 π + 4 πn

x = 2 π + 4 πn

x = 2 π + 4 πn

sin (x) = cos (1 9^{\circ})

\frac{1}{1.5} = \frac{sin ( 3 0 ^{\circ} )}{sin ( x )}, x < 9 0^{\circ}

tan (A) = \frac{8}{15}

tan^{2} (θ) = sec^{2} (θ) + 1

cos (2 B) = \frac{21}{35}, cos (B)

What is the general solution for 0=1+cos(x/2) ?
The general solution for 0=1+cos(x/2) is x=2pi+4pin