How do you find period, amplitude, phase shift and midline of #y = 3 + 2cos(x + (pi/4))#?

1 Answer
Jim G.
Jul 15, 2017

#"see explanation"#

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 shift "=d#

#"here "a=2,b=1,c=pi/4" and "d=3#

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

#"phase shift "=-(pi/4)/1=-pi/4#

#"maximum value "=3+2=5#

#"minimum value "=3-2=1#

#rArr"midline "y=1/2(5+1)=3#

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