Question

Sine function whose period is 6 is​

Answer 1

The period of the sine curve is the length of one cycle of the curve. The natural period of the sine curve is 2π. So, a coefficient of b=1 is equivalent to a period of 2π. To get the period of the sine curve for any coefficient b, just divide 2π by the coefficient b to get the new period of the curve

Answer 2

$\implies \rm{let \: f(x) = sin(kx) }$

$\implies \rm{period \: of \: f(x) = \dfrac{2\pi}{ |k| } = 6}$

$\implies \rm{ \therefore \: \: |k| = \dfrac{\pi}{3} }$

$\implies \boxed{ \boxed{ \rm{ \therefore \: \: f(x)= sin( \dfrac{\pi}{x} ) }}}$