Question

find the period of this equation
y=5sin((x/9)+(pi/6))

Answer 1

let T be required period
then y(x)=y(x+T) where T>0 is the smallest possible
5sin(
x/9+ pi/9)=5sin((x+T)/9+pi/9)
sin( x/9+ pi/9)=sin((x/9)+pi/9+T/9)
so
T/9=2pi ( using sin properties) then T=18*pi