What is the general solution for roots asin(((pi*x))/b) ?

The general solution for roots asin(((pi*x))/b) is x=2bn,x=b(2n+1)

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roots asin(((pi*x))/b)

roots

a sin (\frac{( π \cdot x )}{b})

x = 2 bn, x = b (2 n + 1)

Solution steps

a sin (\frac{( π x )}{b})

The roots are the intercepts with the x-axis

(y = 0)

a sin (\frac{( π x )}{b}) = 0

Solve by substitution

sin (\frac{π x}{b}) = 0

Solve by substitution

sin (\frac{π x}{b}) = 0

Let:

u = \frac{π x}{b}

a sin (u) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

sin (u) = 0

General solutions for

sin (u) = 0

u = 0 + 2 πn, u = π + 2 πn

Solve

u = 0 + 2 πn : u = 2 πn

u = 2 πn, u = π + 2 πn

Substitute back

u = \frac{π x}{b}

\frac{π x}{b} = 2 πn : x = 2 bn; b \neq = 0

\frac{π x}{b} = π + 2 πn : x = b (2 n + 1); b \neq = 0

x = 2 bn, x = b (2 n + 1)

What is the general solution for roots asin(((pi*x))/b) ?
The general solution for roots asin(((pi*x))/b) is x=2bn,x=b(2n+1)