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 height 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 what 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.