# Answer to Question #17133 in Abstract Algebra for brianna

Question #17133

find the period of this equation

y=5sin((x/9)+(pi/6))

y=5sin((x/9)+(pi/6))

Expert's answer

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

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

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