What is the phase shift, vertical displacement with respect to #y=cosx# for the graph #y=cos(x-pi/3)#?

1 Answer
Jim G.
Apr 14, 2017

#" shift of " pi/3to" no vertical displacement"#

Explanation:

The standard form of the #color(blue)"cosine function"# is.

#color(red)(bar(ul(|color(white)(2/2)color(black)(y=acos(bx+c)+d)color(white)(2/2)|)))#

#"where amplitude " =|a|," period " =(2pi)/b#

#"phase shift " =-c/b," vertical displacement " =d#

#"here " a=1,b=1,c=-pi/3,d=0#

#rArr"phase shift "=-(-pi/3)/1=pi/3#

#"with respect to " y=cosx#

#y=cos(x-pi/3)" is " y=cosx" shifted " pi/3" to the right"#

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