Question

How do you find the amplitude, period and phase shift for `y=2sin(theta+45^circ)+1`?

Answer 1

`2,pi,-45^@`

Explanation:

The standard form of the `color(blue)"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 " =(2pi)/b`

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

`"here " a=2,b=1,c=45^@" and " d=+1`

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

`"and phase shift " =-45^@/1=-45^@`