# Trig functions translations and combinations of transfomations word problems

1. Apr 28, 2006

### Aya

Hi, I really need help with this question

1) the water depth in a harber is 21m at hight tide, and 11m at low tide. One cycle is completed approximatly every 12h.

a) find an equation for the water depth as a function of the time, t hours, after low tide
b) Draw a graph 48h after low tide, witch occured at 14:00

y=asink(x-c)+d

Amplitude
a=21-11/2
a=5

K

p=2pi/k
12=2pi/k
k=2pi/12
k=pi/6

what about the c and the d??

and does anyone know of anygood software to graph trig functions?

Thanks

2. Apr 28, 2006

### GregA

Someone else may be able to help you further but for now...

The 'c' is the extent to which the sine function is moved left or right (when t = 0 where is the tide?...what is the value of $$sin(t)$$ when t = 0?)

the 'd' is the extent to which the sine function is moved upwards or downwards...(without any further changes what are the maximum or minimum possible values of $$5sin(t)$$

as for for graphing sine functions (and many other functions) check out this free CAS

3. Apr 28, 2006

### HallsofIvy

Staff Emeritus
"find an equation for the water depth as a function of the time, t hours, after low tide"
In other words, when t= 0 you are at low tide. I think I would be inclined to try just y= asin(t)+ d.

4. Apr 28, 2006

### Staff: Mentor

And modify the argument to the sin() function a little to reflect the period that you are given. The argument to the sin() function should change a total of 2*Pi radians for each period which is 12 hours long.

5. Apr 28, 2006

### Aya

the ansewer in the back of the book is y=5sinpi/6(t-3)+16

But waht I dont understand is how did they know that the graph is moved 3 to the right and 16 units up? I dont understand how they got these numbers from that question, if the low tide is 11m, then would'nt that be the lowest point of the graph making it be 11units up

6. Apr 28, 2006

### GregA

whats the lowest point of $$5sin(t)?$$ and what is the lowest level of the tide?...it isn't actually moved 3 to the right... it is moved $$\frac{\pi}{2}$$ rads to the right
("the ansewer in the back of the book is y=5sinpi/6(t-3)+16")

if you plotted the graph of just $$5sin(\frac{t\pi}{6}) + 16$$ would the high and low tides occur at the correct values of t?

Last edited: Apr 28, 2006
7. Apr 29, 2006

### 0rthodontist

You should get a graphing calculator. I recommend a TI-89 if you want to do any science later.