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Use a graphing calculator to solve the equation in the interval from 0 to 2. Round to the nearest hundredth. 7 cos 2t = 3
i need it step by step to understand it
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.
here it is when i pasted it to google.
i got 6.995735789x
.64 i suppose.
idk about that with google i got .64
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.?
use function manipulation
step bu step if you could
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.
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.
so whats next then
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.
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
yup with you
according to your info 3:30 is high tide. we can call that 3.5
so whats the next step to this problem
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
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|
so should i erase sin and use cos
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 :)
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
so 20*cos(x-3.5)+32 is the final answer
yup did you understand? :)
yes thank you very much for all that help
let me know if it is correct
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
there is also the odds that i need to stretch it horisontally
oh yup you do have to stretch |dw:1356587327217:dw|