Question

The water level varies from 12 inches at low tide to 52 inches at high tide. Low tide occurs at 9:15 a.m. and high tide occurs at 3:30 p.m. What is a cosine function that models the variation in inches above and below the water level as a function of time in hours since 9:15 a.m.?

Answer 1

@phi @amistre64 @Preetha

Answer 2

@rational @SolomonZelman @Preetha @confluxepic

Answer 3

Can one of you help?

Answer 4

start with cosine function and adjust it

Answer 5

how? @amistre64

Answer 6

what does the information tell us?

Answer 7

or rather, what are the parts of a cosine function? how do we write a generic cosine function?

Answer 8

that the min is 12 and the max is 52, right?

Answer 9

good, and the midline is between them

Answer 10

what is the distance from 12 to 52?

Answer 11

strategy

define the most general generic cosine function there is.

use the information in the problem to build that function into the perfect model of the problem.

Answer 12

the distance is 40, so the amplitude is 20

Answer 13

@amistre64

Answer 14

using words instead of letters, the generic cos function is

Amp cos(per(t-phase)) + mid

you found amp, what is midline?

Answer 15

and the most generic cosine function is y=cos(x), right?

Answer 16

no, cos(x) is too specific, there are many more parts to a trig function then x

Answer 17

what do you mean?

Answer 18

i mean what i said

Answer 19

a completly generic cosine function is:

Amp cos(per(t-phase)) + mid

why????

Answer 20

what's (t-phase)?

Answer 21

t is the independant input, and phase is the shifting of the function left or right

Answer 22

do all cosine function have the value cos(0) = 1?

Answer 23

yes?

Answer 24

really

cos(t-pi/2), when t = 0 is equal to 1?

Answer 25

might have misasked the first time.

Answer 26

can functions be shifted left and right?

Answer 27

yes, they can be

Answer 28

how do we shift a function f(x) ?? what gets adjusted?

Answer 29

it depends on the function, right? like a quadratic function shifts if the vertex changes

Answer 30

it doesnt depend on the function, if it did then we could never generalize it.

f(x) shifts left and right by adjust the value of x by some constant

f(x-a) shifts the function to the right by a, why?

let f(x) = k when x=0
f(x-a) = k when x=a
x is shifted to the right by a

Answer 31

x^2 + 1 = 1, when x=0

(x-4)^2 + 1 = 1 , when x=4

(x-4)^2 + 1 is the same function as x^2+1 shifted by +4

Answer 32

cos(t) = 0 when t = pi/2

cos(t - pi/4) = 0 when t = pi/2 + pi/4
^^^^^^

notice that the function is shifted to the right, by pi/4

Answer 33

okay