What is the general solution for sin(10x)=0 ?

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

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sin(10x)=0

sin (10 x) = 0

x = \frac{πn}{5}, x = \frac{π}{10} + \frac{πn}{5}

Degrees

x = 0^{\circ} + 3 6^{\circ} n, x = 1 8^{\circ} + 3 6^{\circ} n

Solution steps

sin (10 x) = 0

General solutions for

sin (10 x) = 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}

10 x = 0 + 2 πn, 10 x = π + 2 πn

10 x = 0 + 2 πn, 10 x = π + 2 πn

Solve

10 x = 0 + 2 πn : x = \frac{πn}{5}

10 x = 0 + 2 πn

0 + 2 πn = 2 πn

10 x = 2 πn

Divide both sides by

10

10 x = 2 πn

Divide both sides by

10

\frac{10 x}{10} = \frac{2 πn}{10}

Simplify

x = \frac{πn}{5}

x = \frac{πn}{5}

Solve

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

10 x = π + 2 πn

Divide both sides by

10

10 x = π + 2 πn

Divide both sides by

10

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

Simplify

x = \frac{π}{10} + \frac{πn}{5}

x = \frac{π}{10} + \frac{πn}{5}

x = \frac{πn}{5}, x = \frac{π}{10} + \frac{πn}{5}

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