Please help me (sin graph)

[limber chasm]

and if possible may i get a quick explanation for each? id really appreciate it, thank you so much

[hallow ice]

compare it to the general rorm of a sine wave

A is 1/2 the distance from max to min so since its 10 from max to min you know A is 5

periods just 2pi/b

phase shift is in the same vein how far away from a normal sine curve

[limber chasm]

whast the difference between phase shift and veritical shift?

[limber chasm]

also how do i find the frequency b?

[hallow ice]

phase shift changes the ocsilation

vertical moves it along the y axis

[limber chasm]

how do i find those based off this graph? would i need to find the graph equation first?

[hallow ice]

youre gettinf the equation from the graph

[limber chasm]

so how would i find the frequency factor b and both the shifts?

[hallow ice]

the distance it takes to reach the same point again and the shift is tje distance from a normal sine wave

[limber chasm]

im kind of confused how youd get that though, sorry

[hallow ice]

a normal sine wave goes from -1 to 1 you tale the averwhe to fimd the midline

so since this is from -26 to -16 the midline is 5 away from both or at y=-21

so we know d is -21

[limber chasm]

ahh i see thats the vertical shift

[hallow ice]

to find the period youd see long it would take to repeat a value so its -16 at -10 and its back at -16 again at 6 so the period is 16 and thats our B value and from that we divde 2pi by it so itz 2pi/16 or pi/8

so I dont get lost im just gonna type it out

[limber chasm]

ohh i see that makes so much sense thank you

and howd would you find the phase shift lastly?

[hallow ice]

distance between critial points

0,pi/2,pi,3pi/2,2pi etc...

[limber chasm]

how would i find the difference between them in this graph

[hallow ice]

set the inside equal to zero

[limber chasm]

im sorry i dont understand 😭

inside of the graph equal to 0?

[hallow ice]

sorry that was a mistake on my end

[limber chasm]

also you mean the frequency factor is 16 and thats our B value right?

[hallow ice]

yes

[limber chasm]

okay thank you

[limber chasm]

we have the vertical shift as -21, do we use this to get the phase shift?

[hallow ice]

no

the phase shift is just how far away the curve is from the oarent graph

so lets look at sine of zero

we know it has to be zero at zero but this graph is zero at -2

well a min

but you know what I mean

[limber chasm]

yah the minimum at -2

[hallow ice]

so we then set up the insixe of the function (bx-c) and set it equal to that shift of -2 so it becomes pi/8x=-2 which yields the phase shift is -pi/4

[limber chasm]

oh so to find the phase shift, we find the minimum y value and then set it equal to the frequency factor and solve?

[hallow ice]

no, to fimd ps we just find out how far offset the graph is from the parent functions critical points

i just used the min as its easier

but any of them would have worked

[limber chasm]

so does this not work with every graph?

[hallow ice]

no phase shift is just setting the bx-c term equal to zero

we use the min and max values yo find the midline

[limber chasm]

ah okay okay thank you so much for the help

[hallow ice]

np

[limber chasm]

also one more question @hallow ice

sorry for the bother but

how would you find amplitude based off minimum and maximum points of a sin graph

like if max was (4.5, 2) and minimum was (1.5, 22)

[hallow ice]

the amplitude is the distance from the midline from max to min

so youd average it out

so A would ve there 3

and youx have a vertical ahift of 1.5 up

[limber chasm]

oh i thought wed have to look at y values like before

not the x values

[hallow ice]

no, x values are for finding phase shift

[limber chasm]

so wouldnt a be 10

and vertical shift be 12

[hallow ice]

what?

[limber chasm]

amplitiude is half the distance from maximum to minmum value

so 20/2

[hallow ice]

ph

i misread

yes

it would be

the average of them

so 20+2/2

or 11

[limber chasm]

oh not 22-2/2

[hallow ice]

yeah

wajt

did you mean -20?

either way amplitude just tells you how tall it is

[limber chasm]

point is 1.5,22 so 22

but i get it now, thank you!!

[limber chasm]

hello again @hallow ice 😭

if i have a graph like this

with these as data points

how do i just find the phase shift