How do you find the amplitude, period, and shift for #y=2sin(x-45°)-1#?

1 Answer
Jim G.
May 19, 2018

#2,360^@,45^@,-1#

Explanation:

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

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

#"here "a=2,b=1,c=-45^@" and "d=-1#

#"amplitude "=|2|=2," period "=360^@/1=360^@#

#"phase shift "=-(-45^@)/1=45^@,"vertical shift "=-1#

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