Question

Need help with Modelling trigonometric function Question is in attached image

Answer 1

The answer the book give is y=16.2 sin (2pi/365(x-116))+1.4 I got all the same number except the -116

Answer 2

Anyone know how they got -116?

Answer 3

I got 1.1475... for the value of the phase shift

Answer 4

okay back

Answer 5

Out of curiosity, how do you find the numbers you did find ?

Answer 6

I chose one of the points from the table given and then solved for the phase shift variable d

Answer 7

and i got 1.4475

Answer 8

1.1475*

Answer 9

how did you find the 16.2, etc

Answer 10

max value-min value divided by 2

Answer 11

and the vertical shift is max value + min value divided by 2

Answer 12

the horizontal stretch/comp factor I found using period which is 365 days and the formula for period=2pi/k

Answer 13

k=horizontal stretch/comp factor

Answer 14

so yea i dont know how they got the horizontal phift

Answer 15

shift*

Answer 16

any idea on how they got the value?

Answer 17

I am thinking about it

Answer 18

my first thought is to check that
y=16.2 sin (2pi/365(x-116))+1.4
actually works.

what should we use for x to check the january value ?

Answer 19

1

Answer 20

i got -13.46, anyone else confirm that?

Answer 21

i got the -14.8 before adding 1.4

Answer 22

so something is off

Answer 23

maybe we should use the middle of the month, say day 15 ?

Answer 24

okay

Answer 25

i got close to it -14.5

Answer 26

yes, but it's hard to see a simple way to figure out the best phase shift so we minimize the error between the table and our sin function.

Answer 27

so we can't pin point the exact phase shift

Answer 28

im bored with this question, im just going to ask my teacher to do this on the board. Time to move on Thanks for helping :)

Answer 29

you also have to figure out the interval where the temps < 0 degrees