Trig functions translations and combinations of transfomations word problems

[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 occurred 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

 

[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
http://maxima.sourceforge.net/download.shtml

 

[HallsofIvy]

"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.

 

[berkeman]

y= asin(t)+ d.

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.

 

[Aya]

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

But waht I don't understand is how did they know that the graph is moved 3 to the right and 16 units up? I don't 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

 

[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?

 

[0rthodontist]

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

Thanks

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