What is the phase shift, vertical displacement with respect to $y = cos x$ $y=cosx$ for the graph $y = cos (x - \frac{π}{3})$ $y=cos(x-pi/3)$ ?

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What is the phase shift, vertical displacement with respect to $y = cos x$ $y=cosx$ for the graph $y = cos (x - \frac{π}{3})$ $y=cos(x-pi/3)$ ?

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Answer 1 · 2017-04-14T10:44:21

$shift of \frac{π}{3} \to no vertical displacement$ $" shift of " pi/3to" no vertical displacement"$

Explanation:

The standard form of the $cosine function$ $color(blue)"cosine function"$ 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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What is the phase shift, vertical displacement with respect to $y = cos x$ $y=cosx$ for the graph $y = cos (x - \frac{π}{3})$ $y=cos(x-pi/3)$ ?

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Explanation:

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What is the phase shift, vertical displacement with respect to y=cosxy=cosxy=cosx for the graph y=cos(x-pi/3)y=cos(x−π3)y=cos(x-pi/3)?

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What is the phase shift, vertical displacement with respect to $y = cos x$ $y=cosx$ for the graph $y = cos (x - \frac{π}{3})$ $y=cos(x-pi/3)$ ?