Question

Please please please help
What is the amplitude, period, and phase shift of f(x) = −3 cos(4x + π) + 6?

Answer 1

you want to use the form
\[f(x)=Acos(kx-\omega t+\phi _{0} )\]
A:amplitude
k:wave number
x_position
w:angular frequency
t:time
phi_0:phase

Answer 2

do you mind walking through it or explaining it, because i don't really understand any of that... learning math online is very difficult on your own. @VeritasVosLiberabit

Answer 3

sure. for one the easiest one to spot is the amplitude: -3 but since amplitude is always positive the amplitude is 3

Answer 4

for the period I think you have to find x when 4x=2pi
so the period is
\[x=\frac{ 2\pi }{ 4 }\]
and the phase is the tacked onto 4x which is pi in this case.

Do you have an answer bank, because I'm not 100% on this and want to make sure its correct

Answer 5

amplitude = 3; period = pi over two; phase shift: x = negative pi over four

amplitude = −3; period = pi over two; phase shift: x = pi over four

amplitude = −3; period = negative pi over two; phase shift: x = negative pi over four

amplitude = 3; period = 2π; phase shift: x = negative pi over four

Answer 6

the final answer should be
\[A=3,T=\frac{ \pi }{ 2 },\phi _{0}=\pi \]

Answer 7

ah ok so there is something off but close let me look

Answer 8

looks like th closest one to your answer is A?

Answer 9

I'm not sure where the -(pi)/4 is coming from though I need to think for a moment

Answer 10

okay

Answer 11

hm maybe its not 4x=2pi for period but I think the answer is the same
\[\frac{ 2\pi }{ T }=4\] is the period because that is what w is
solve for T which is \[\frac{ \pi }{ 2 }\]

Answer 12

so A must be right but the -(pi)/4 I'm not so sure about

Answer 13

okay thank you for the help i appreciate it!! Do you mind helping with one more?

Answer 14

sure make a new thread and link me

Answer 15

Oh I think i see for the phase now
you do \[4x+\pi=0\] and solve for x it seems