What is a algebraic proof that the period for sine function is 2π/b?

Answer 1

Let f(x) = Asin(Bx + C)

f(x + 2π/B) = Asin(B(x + 2π/B) + C) = Asin(Bx + 2π + C) = Asin[(Bx+C) + 2π] =

A{sin(Bx + C)cos(2π) + cos(Bx+C)sin2π} = A{sin(Bx+C)(1) + cos(Bx+C)(0)} = Asin(Bx + C) = f(x)

So, the value of f(x) repeats every 2π/B units.