What is the general solution for roots sin(ax) ?

The general solution for roots sin(ax) is x=(2pin)/a ,x= pi/a+(2pin)/a ;\quad a\ne 0

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roots sin(ax)

roots

sin (a x)

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

Solution steps

sin (a x)

The roots are the intercepts with the x-axis

(y = 0)

sin (a x) = 0

General solutions for

sin (a x) = 0

a x = 0 + 2 πn, a x = π + 2 πn

Solve

a x = 0 + 2 πn : x = \frac{2 πn}{a}; a \neq = 0

Solve

a x = π + 2 πn : x = \frac{π}{a} + \frac{2 πn}{a}; a \neq = 0

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

\int \frac{( 1 - 3 x )}{2 x - 3 x ^{2}} d x

\frac{d}{d x} (- \frac{2}{x ^{2} + 1})

\frac{d y}{d x} = \frac{( x - 3 )}{( y + 1 )}

f (x) = \frac{1}{( 1 + x ^{2} )}

\frac{x ^{2} - 3 x + 2}{- x ^{2} - 4 x - 4}

What is the general solution for roots sin(ax) ?
The general solution for roots sin(ax) is x=(2pin)/a ,x= pi/a+(2pin)/a ;\quad a\ne 0