Question

Find a sine function whose period is $\frac{2}{3}$.

Answer 1

periodic function is a special type of function in which, function returning to the same value at regular intervals. for any function y = f(x) , T will be period only when f(x) = f(x + T).

we know , if period of function y = f(x) is T then period of function y = f(ax ± b) will be T/|a|

we have to find a sine function whose period is 2/3

there are many possibilities .

Let's find a sine function,

period sine function is 2/3 , but we know period of sinx is 2π
it means, coefficient of sine function definitely contains 3π

so, function should be f(x) = sin(3πx)