Question

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

Answer 1

HINT: The given periodic function:

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

will have

Amplitude `=2`

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

Phase shift `=-45`

Answer 2

`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^@`