What is the amplitude, period and the phase shift of # f(x)= 3sin(2x + pi)#?

2 Answers
Jim G.
Apr 21, 2017

#3,pi,-pi/2#

Explanation:

The standard form of the #color(blue)"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=3,b=2,c=pi,d=0#

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

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

Narad T.
Apr 21, 2017

The amplitude is #A=3#
The period is #=pi#
The phase shift is #=-(pi)/(2)#

Explanation:

#y = A sin(Bx + C) + D#

Amplitude is #A#

Period is #(2π)/B#

Phase shift is #−C/B#

Vertical shift is #D#

Here, we have

#y=3sin(2x+pi))#

#y=3sin(2x+pi)#

The amplitude is #A=3#

The period is #=(2pi)/B=(2pi)/(2)=pi#

The phase shift is #=-(pi)/(2)#

graph{3sin(2x+pi) [-5.546, 5.55, -2.773, 2.774]}

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