What is the general solution for 1/2 sin(x/5)=0 ?

The general solution for 1/2 sin(x/5)=0 is x=10pin,x=5pi+10pin

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1/2 sin(x/5)=0

\frac{1}{2} sin (\frac{x}{5}) = 0

x = 10 πn, x = 5 π + 10 πn

Degrees

x = 0^{\circ} + 180 0^{\circ} n, x = 90 0^{\circ} + 180 0^{\circ} n

Solution steps

\frac{1}{2} sin (\frac{x}{5}) = 0

Multiply both sides by

2

\frac{1}{2} sin (\frac{x}{5}) = 0

Multiply both sides by

2

2 \cdot \frac{1}{2} sin (\frac{x}{5}) = 0 \cdot 2

Simplify

sin (\frac{x}{5}) = 0

sin (\frac{x}{5}) = 0

General solutions for

sin (\frac{x}{5}) = 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}{5} = 0 + 2 πn, \frac{x}{5} = π + 2 πn

\frac{x}{5} = 0 + 2 πn, \frac{x}{5} = π + 2 πn

Solve

\frac{x}{5} = 0 + 2 πn : x = 10 πn

\frac{x}{5} = 0 + 2 πn

0 + 2 πn = 2 πn

\frac{x}{5} = 2 πn

Multiply both sides by

5

\frac{x}{5} = 2 πn

Multiply both sides by

5

\frac{5 x}{5} = 5 \cdot 2 πn

Simplify

x = 10 πn

x = 10 πn

Solve

\frac{x}{5} = π + 2 πn : x = 5 π + 10 πn

\frac{x}{5} = π + 2 πn

Multiply both sides by

5

\frac{x}{5} = π + 2 πn

Multiply both sides by

5

\frac{5 x}{5} = 5 π + 5 \cdot 2 πn

Simplify

x = 5 π + 10 πn

x = 5 π + 10 πn

x = 10 πn, x = 5 π + 10 πn

sin (\frac{1}{3} x) = 0, 0 \leq x \leq 10 π

sin (π y) = cos (1) sin (\frac{π}{6}) - \frac{1}{2}

0 = 4 cos (120 x)

(2 sin (x) - 1) (cos (x) - 2) = 0

7 - 6 sin (x) = 3 + 2 sin (x)

What is the general solution for 1/2 sin(x/5)=0 ?
The general solution for 1/2 sin(x/5)=0 is x=10pin,x=5pi+10pin