Question 1159753
In comparison to the graph {{{y=3cos(x)}}}, specifically describe the type of transformation of the graph of {{{y=3cos(x+pi/3)}}}

Let us first look at {{{y=3cos(x)}}}

 compare it  to {{{y = A cos (Bx + C) }}}

{{{A = 3}}}... amplitude
{{{B = 1}}}.........If B is equal to 1, then it takes 2pi to complete a period; so, a period is 2pi
 {{{C = 0}}}.........no horizontal displacement (or shift)

It is easy to characterize the effect of changes in {{{C}}}  as a mapping  ({{{x}}}, {{{y}}})  to ({{{x + C}}}, {{{y}}}) and this is a translation either moving the graph to the left if C is positive, or to the right if {{{C}}} is negative.

now look at {{{y=3cos(x+pi/3)}}}  compare it  to {{{y=3cos(x)}}}

only difference is the value of {{{C }}}which is {{{pi/3}}}, so {{{C>0 }}}

 and this is a translation moving the graph {{{pi/3}}} to the {{{left }}} 


{{{drawing( 600, 600, -5, 5, -5, 5,
locate(1,2,highlight(y=3cos(x))),locate(1,-2,highlight(green(y=3cos(x+pi/3)))),
 graph( 600, 600, -5, 5, -5, 5, 3cos(x), 3cos(x+pi/3))) }}}