## tkachenko 2 years ago i need a little help

• This Question is Open
1. tkachenko

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

2. tkachenko

i need it step by step to understand it

3. timo86m

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.

4. timo86m
5. timo86m

here it is when i pasted it to google.

6. tkachenko

i got 6.995735789x

7. timo86m

.64 i suppose.

8. timo86m

9. tkachenko

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.?

10. timo86m

use function manipulation

11. tkachenko

step bu step if you could

12. timo86m

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.

13. timo86m

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.

14. tkachenko

so whats next then

15. timo86m

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.

16. timo86m

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

17. tkachenko

yup with you

18. timo86m

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

19. tkachenko

so whats the next step to this problem

20. timo86m

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

21. timo86m

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|

22. tkachenko

so should i erase sin and use cos

23. timo86m

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 :)

24. timo86m

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

25. tkachenko

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

26. timo86m

yup did you understand? :)

27. tkachenko

yes thank you very much for all that help

28. timo86m

let me know if it is correct

29. tkachenko

okay

30. timo86m

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

31. tkachenko

its okay

32. timo86m

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

33. timo86m

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