Question

what is the amplitude, period, and phase shift of f(x)=-3cos(4x+pie)+6 ?

i need help step by step please

Answer 1

@perl

Answer 2

@dtan5457

Answer 3

Let's consider a more general case. Take \(f(x)=a\cos (b(x-c))+d\).

The amplitude is \(|a|\), the period is \(\dfrac{2\pi}{b}\), the horizontal/phase shift if \(c\), and the vertical shift is \(d\). (The same works for \(\sin\)).

Answer 4

i dont quite understand...((omg your a sith lol starwars is awesome))

Answer 5

@SithsAndGiggles

Answer 6

If we want to make a direct connection between the general form and the particular function you're given, it's a matter of writing the function accordingly.

It should be clear to you that \(a=-3\). What's the value of \(|a|\)? (This is your amplitude.)

To find the period, we need the coefficient of \(x\) to be \(1\), but we're given \(4\). Factorizing, we get
\[4x+\pi=4\left(x+\frac{\pi}{4}\right)\]
so we have that \(b=4\), and additionally that \(c=-\dfrac{\pi}{4}\). What are the period and phase shifts going to be?

You don't have to worry about the vertical shift \(d\), but it's apparent that \(d=6\) and so the curve is shifted \(6\) units up.

Answer 7

so would my answer be
amplitude = 3
period= pi/2
phase shift : x = - pi/4

Answer 8

@sithsandgiggles

Answer 9

@dtan5457

Answer 10

@GracieBugg

Answer 11

There is no way that I can answer this ,I suck that bad at math xD sorry!

Answer 12

I'm sorry @hailhydra
I really wish I could help, but I haven't learnt that, yet. I'm soo sorry

Answer 13

@dan815

Answer 14

@Michele_Laino

Answer 15

aww , thanks for letting me know though haha :) @Music_me

Answer 16

Yes your answer is right.

Answer 17

thank you so much @SithsAndGiggles so so so much!~

Answer 18

@sithandgiggles

Answer 19

*sithsandgiggles

Answer 20

@sithsandgiggles

Answer 21

wait! i just noticed isnt the amplitude equal -3 ? i thinky ou misread it

Answer 22

@dan815

Answer 23

@dan815

Answer 24

@jim_thompson5910

Answer 25

@amistre64

Answer 26

@aaronq

Answer 27

@jim_thompson5910 can you help clarify this last part for me?

Answer 28

what's your question?

Answer 29

what is the amplitude, period, and phase shift of f(x)=-3cos(4x+pie)+6 ?

Answer 30

how much do you have so far

Answer 31

@jim_thompson5910

Answer 32

hint:

y = A*cos(Bx - C) + D

|A| is the amplitude
T = 2pi/B is the period
C/B is the phase shift
y = D is the midline

Answer 33

oh I see you wrote

`so would my answer be`
` amplitude = 3 `
` period= pi/2`
` phase shift : x = - pi/4`

Answer 34

amplitude = 3 is correct
period= pi/2 is correct
For the phase shift, I would simply just say "-pi/4 units"

Answer 35

so would my answer be
amplitude = -3
period= pi/2
phase shift : x = - pi/4

Answer 36

isnt the amplitude -3?

Answer 37

@jim_thompson5910

Answer 38

no the amplitude is always positive

it's a distance

Answer 39

|A| = |-3| = 3

Answer 40

ohhhhhhhhhhhhhhhhh okk thank you i checked it in my notes thank you @jim_thompson5910

Answer 41

np

Answer 42

@jim_thompson5910

Answer 43

@amistre64

Answer 44

hey, i was wondering if you can explain to me how the period is found?

Answer 45

well, what is your concept of periodic?

Answer 46

like it measures time?

Answer 47

1 period is defined as the time it takes to start over again ..... agreed?

Answer 48

if we take the smallest interval as the fundamental periodic rate then...

we have to ask outselves; when does trig(0) = trig(a) ??

then the period is defined as 'a'

Answer 49

you have cos(u) for whatever the inside is ...

what is the first time that cos(0) = cos(a) ??

Answer 50

im not grasping the understanding of your question :(

Answer 51

wht is the value of cos(0) ?

Answer 52

is it 0 or 1?

Answer 53

could it be that there is no cos ?

Answer 54

no there is a cos, for whatever that means

and its not my responsibility to know cos(0) at the moment ... you tell me the value of cos(0) and ill correct you.

Answer 55

is it equal to 1?

Answer 56

cos(0) = 1

now, the period of cos is the value 'a' such that cos(a) = 1 for the first time again .... assume x is on an interval from 0 to a

Answer 57

is cos(pi/4) = 1 ?
is cos(pi/3) = 1 ?
is cos(pi/2) = 1 ?
is cos(pi) = 1 ?
is cos(3pi/2) = 1 ?
is cos(2pi) = 1 ?

Answer 58

is it is cos(pi/2) = 1

Answer 59

good, then cos(0) = cos(2pi) is the smallest interval in which cos repeats itself.

cos(u) has a normal period of 2pi

now, lets use this to determine the distance in your problem

let u = 4x+pi

when u1 = 0 when x=?
when u2 = 2pi when x=?

and therefore the period is u2-u1

Answer 60

isnt the distance the amplitude = 3

Answer 61

of course not, the distance along the x axis does not measure height (amplitude)

Answer 62

im a little confused