How do you graph and list the amplitude, period, phase shift for #y=2cos(2x-45)#?

2 Answers
Harish Chandra Rajpoot
Jul 12, 2018

HINT: The given periodic function:

#y=2\cos(2x-45)#

will have

Amplitude #=2#

Period #={2\pi}/2=\pi#

Phase shift #=-45#

Jim G.
Jul 12, 2018

#2,180^@,22.5^@#

Explanation:

#"the standard form of the 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 "=360^@/b#

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

#"here "a=2,b=2,c=-45^@" and "d=0#

#"amplitude "=|2|=2," period "=360^@/2=180^@#

#"phase shift "=-(-45^@)/2=22.5^@#

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