Question

How do you find the amplitude, period and phase shift for `y=1/2cos(theta+90^circ)`?

Answer 1

`"amplitude "=1/2,"period "=360^@," phase shift "=-90^@`

Explanation:

The standard form of the `color(blue)"cosine function"` is.

`color(red)(bar(ul(|color(white)color(black)(y=acos(bx+c)+d)color(white)(2/2)|)))`

`"where amplitude "=|a|," period "=(360^@)/b`

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

`"here "a=1/2,b=1 ,c=90^@,d=0`

`rArr"amplitude "=|1/2|=1/2," period "=(360^@)/1=360^@`

`"phase shift "=-90^@/1=-90^@`