Question 419958
The {{{b}}} in both of the graph types

 {{{y = a sin bx}}}
 {{{y = a cos bx}}}

affects the {{{period}}} (or wavelength) of the graph. 

The {{{period}}} is the distance (or time) that it takes for the sine or cosine curve to begin repeating again.

The period is given by:

    math expression  {{{period=2(pi)/b}}}

Note: As {{{b}}} gets larger, the period {{{decreases}}}.


What is the period of {{{y=(1/3)cos (x/2)}}}



since {{{bx= x/2}}}....->..{{{b= 1/2}}, b tells us the number of cycles in each 2π.

then

{{{period=2(pi)/b}}}

{{{period=2(pi)/(1/2)}}}


{{{period=2(3.14)/(1/2)}}}


{{{period=6.28/(1/2)}}}


{{{period=2*6.28}}}


{{{period=12.56)}}}