Question

y = sin (1/4) (x+(Ï€/3))

What is the period of this function?

y = sin (1/4) (x+(Ï€/3))

What is the period of this function?

@Mathematics

Answer 1

For functions of the form\[f(x) = A\sin(\omega x + \delta)\] the period of the function is \[T = \frac{2\pi}{\omega}\] so for you, since
\[f(x) = \sin(\frac{x+\frac{\pi}{3}}{4}) = \sin(\frac{1}{4}x+\frac{\pi}{12})\]
you have\[T = \frac{2\pi}{\omega} = \frac{2\pi}{\frac{1}{4}} = 8\pi\]