Question

Find the amplitude and the phase shift of the function f(x) = - 3sin(2x + π/2)

Answer 1

using the general equation \[f(x)=asin(bx-c)+d

a is the amplitude, it measures how high and low the function goes aka max and mins. In otherwords if you had amplitude 3 , it would mean that the graph would max at 3 and min a -3

Answer 2

phase shift is when x-c =0

Answer 3

so for amplitude you have a=-3 so amplitude equates to -3. This means that the sine function is a mirror image of the regular function. It starts downwards rather than upwards.

as for phase shift you need to be careful with b. If it's 1 , then you can simply say

x-c=0 or x=c.

another example

x-(-c)=0
x+c=0
x=-c

Answer 4

when you have a b that is not 1 i simply pull it out so now you get

\[-3sin(2(x+\frac{\pi}{4}))\]

Answer 5

so, now you have

\[x+\frac{\pi}{4}=0\]
\[x=\frac{-\pi}{4}\]

Answer 6

that is your phase shift

Answer 7

ty!!!