How do you find the amplitude, period, and shift for #y=1/3 sin (2x - pi/3)#?

2 Answers
Dec 21, 2017

See below.

Explanation:

If we write a trigonometric equation in the form:

#y=asin(bx+c)+d#

Then:

Amplitude is a

Period is #(2pi)/b#

Phase shift is #(-c)/b#

Vertical shift is d

From example:

Amplitude #=a=1/3#

Period # = (2pi)/b=pi#

Phase shift # = (-c)/b=(pi/3)/2=pi/6#

Vertical shift # = d =0# no vertical shift.

Dec 21, 2017

#1/3,pi,pi/6,0#

Explanation:

#"the standard form of the sine function is"#

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

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

#"phase shift "=-c/b" and vertical shift "=d#

#"here "a=1/3,b=2,c=-pi/3,d=0#

#rArr"amplitude "=|1/3|=1/3," period "=(2pi)/2=pi#

#"phase shift "=-(-pi/3)/2=pi/6#

#"there is no vertical shift"#