i need a little help

- anonymous

i need a little help

- schrodinger

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- anonymous

Use a graphing calculator to solve the equation in the interval from 0 to 2. Round to the nearest hundredth.
7 cos 2t = 3

- anonymous

i need it step by step to understand it

- anonymous

just type in
7* cos (2x)
and where the graph crosses 3 is your answer. Make sure you in radians. Or degrees depends on what your q asks.

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## More answers

- anonymous

http://www.google.com/search?q=7*+cos+(2x)&rlz=1C1CHFX_enUS470US470&oq=7*+cos+(2x)&sugexp=chrome,mod=1&sourceid=chrome&ie=UTF-8

- anonymous

here it is when i pasted it to google.

- anonymous

i got 6.995735789x

- anonymous

.64 i suppose.

- anonymous

idk about that with google i got .64

- anonymous

what about this one 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.?

- anonymous

use function manipulation

- anonymous

step bu step if you could

- anonymous

ok lets see if we can do this
start with the graph of sin x
|dw:1356583876231:dw|
Lets see if we can manipluate it.

- anonymous

the rules are
a*sin (x) a streches it up and down
1/a sin (x) shrinks it.
a+sin(x) shifts it up
-a+sin(x) shifts it down
sin(x+a) shifts to the left TO the LEFT
now lets combine those rules.

- anonymous

so whats next then

- anonymous

1----
if you with me so far lets start
The water level varies from 12 inches at low tide to 52 inches at high tide
52-12= 40 this gives us our amplitude which is difference
so we get this
40*sin(x) http://tinyurl.com/dyqaluu <-graph
but we want half of that cuzz of this
|dw:1356585003441:dw|
so
now we have
20*sin(x)
2----
now we shift it up
before i shift it up are you with me so far?
there are a few more steps. shifting up and shifting left.

- anonymous

2-- shifting up
so far we have this http://tinyurl.com/dyqaluu
20*sin(x)
If you look at it the low point aka low tide is at -20 put we want it at +12
so we have shift up by an unknown amount we set up this equation
-20+x=12 in my mind i read it as add x to -20 till you get 12
x=32
so now we have
20*sin(x)+32
with me so far.
notice it getting more and more looking like our wanted graph now we shift left and right. With me so far?
http://tinyurl.com/cpcmz73 graph

- anonymous

yup with you

- anonymous

according to your info 3:30 is high tide.
we can call that 3.5

- anonymous

so whats the next step to this problem

- anonymous

Using 20*sin(x)+32 we have to get the hide tide to occur at 3.5 we shift it
20*sin(x-a)+32

- anonymous

ooh i noticed i messed up a bit by using sin. Using cos will be easier cuzz the amplitude is right at 0 hour |dw:1356585955086:dw|

- anonymous

so should i erase sin and use cos

- anonymous

so just shift to right 3.5
so final answer is
20*cos(x-3.5)+32
^
remember adding actually shifts to the left and subtracting shift right :)

- anonymous

yes use cos. Cos is nothing but sin shifted a certain amount to the left or right so that the coordinant of is 0,1 not 0,0

- anonymous

so 20*cos(x-3.5)+32 is the final answer

- anonymous

yup did you understand? :)

- anonymous

yes thank you very much for all that help

- anonymous

let me know if it is correct

- anonymous

okay

- anonymous

fan me so you dont lose touch. I am really interested in this problem. Have not done it in years. I am 99.99999999% sure it is right but since i have not done it in a while. there is still that .0000000000001% possibility i am rusty :D

- anonymous

its okay

- anonymous

there is also the odds that i need to stretch it horisontally

- anonymous

oh yup you do have to stretch
|dw:1356587327217:dw|

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