What is the general solution for -sin(x/2)=0 ?

The general solution for -sin(x/2)=0 is x=4pin,x=2pi+4pin

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-sin(x/2)=0

- sin (\frac{x}{2}) = 0

x = 4 πn, x = 2 π + 4 πn

Degrees

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

Solution steps

- sin (\frac{x}{2}) = 0

Divide both sides by

- 1

- sin (\frac{x}{2}) = 0

Divide both sides by

- 1

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

Simplify

sin (\frac{x}{2}) = 0

sin (\frac{x}{2}) = 0

General solutions for

sin (\frac{x}{2}) = 0

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

\frac{x}{2} = 0 + 2 πn, \frac{x}{2} = π + 2 πn

\frac{x}{2} = 0 + 2 πn, \frac{x}{2} = π + 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

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 = 4 πn, x = 2 π + 4 πn

cos (x) cot (x) = cos (x) cot (3 x - 50)

7 (2 sin^{2} (x) - 1) = 0

cos (a) = \frac{- 3}{2}

2 cos (2 c) = \frac{( 0 ) - ( 0 )}{( π ) - ( - π )}

- 5 cos (2 θ) - 9 sin (θ) + 8 = - sin (θ)

What is the general solution for -sin(x/2)=0 ?
The general solution for -sin(x/2)=0 is x=4pin,x=2pi+4pin