Need this question answered a.s.a.p

Alive · 2010-10-22 21:14:13

The depth of water d metres in a river, at a time t hours after 12 noon, 400. is given by d(t) = 5cos(πt / 12)
[π is pi]

a) sketch the graph of d(t) against t, showing one cycle on the axes, clearly marking in suitable areas

b) state the period and amplitude of depth of water

c) State the highest level of water and the time of day when this occurs

d) State the lowest level of water and time of day when this occurs

e) by solving an appropriate trigonometric equation, find time of day when level of water in river is equal to 2.5 metres

PLEASE DO THIS QUESTION FOR ME, I HAVE TO STUDY FOR OTHER EXAMS AND WON'T HAVE THE TIME TO ACTUALLY FOCUS IN QUESTIONS LIKE THIS, THIS QUESTION WILL BE A LIFE SAVER.. LAST WEEK, PLEASE DO THIS QUESTION FOR ME.

Last edited by Alive (2010-10-22 23:26:20)

bobbym · 2010-10-22 21:23:16

Hi Alive;

5cos(π / 12) is a constant, what varies here?

I HAVE TO STUDY FOR OTHER EXAMS AND WON'T HAVE THE TIME TO ACTUALLY FOCUS IN QUESTIONS LIKE THIS,

Cannot say I agree with that. Math is the most important! What else can you be studying that relegates math to "I do not have the time?"

Alive · 2010-10-22 22:17:15

Yes i agree with you and I shouldn't have postponed it. There's many other exams to do and I need this question. The thing is that it will take a long time to actually understand the steps just for one question which I can try to understand after the exams.

What varies there? I seriously don't know.

bobbym · 2010-10-22 22:19:41

Have you copied the problem correctly? You see you have no independent variable t. Meaning there is no t on the right.

This what your graph will look like.

http://www.mathsisfun.com/graph/functio … 6666666667

Just a horizontal line with a constant value of about 4.82. Not very interesting.

Either you left out a t on the right or it is d'(t) = 5cos(π / 12)

Alive · 2010-10-22 23:27:46

Oh my mistake, it really is d(t) = 5cos(πt / 12)
And i also didn't add 400 after 12 noon. I edited my first post.
Could you do it again please?

bobbym · 2010-10-22 23:30:00

Hi

What is 400?

Alive · 2010-10-22 23:43:53

Actually ignore the 400 part, I think i accidentally copied the question wrong. It's just d(t) = 5cos(πt / 12)
Will that make sense without 400?

Last edited by Alive (2010-10-22 23:45:00)

bobbym · 2010-10-22 23:46:57

Much more sense. I will try as many parts as I can. It will take some time.
Also are you sure that I am not dealing with a differential equation?

Alive · 2010-10-22 23:54:41

Our topic was Circular (trigonometric) functions
>Measuring angles in degrees and radians
>Definining circular functions: sine and cosine
> Another circular function: Tangent
> Symmetry properties of circular functions
>Exact values of circular functions
> Graphs of sine and cosine
Sketch graphs of y = a sin n(t+_ e) and y = a cos n(t+_e)
>Solution of trigonometric equations
>Further symmetry properties
>Tangent function
>Applications of trigonometric functions.

I don't remember doing differential equations, and thank you :]

Last edited by Alive (2010-10-22 23:55:03)

bobbym · 2010-10-22 23:59:48

Hi;

Okay, it is not a differential equation. Thought maybe a little apostraphe had been left out.

e) This first cycle occurs at t = 4 hours and every 24 hours after that.
The second cycle occurs at t=20 and every 24 hours after that.

Alive · 2010-10-23 00:00:10

Oh and if it is going to take a really long time then don't worry about it bobbym, you're a really nice person and I thought it was an easy question the teacher gave us. This is the only question I didn't do, didn't study and I should be able to pass hopefully because i'm sure with my answers for other questions. I just don't want you to waste your time, Time is precious

bobbym · 2010-10-23 00:13:30

Hi Alive;

Do not worry about the time, there is time enough.
The problem is d) It does not make sense. There is some constant that must be added to your function.

You see the minimum in the drawing. It has about - 4 meters of water. Such a thing is not possible.

Alive · 2010-10-23 00:21:45

I am sure that i copied down the question wrong.... It's my fault lol.. I'll post my other question and answers tomorrow so that you can give your opinion if their correct or not

Last edited by Alive (2010-10-23 00:22:17)

bobbym · 2010-10-23 00:25:14

Okay, do you want me to wait until when you post the correct problem.

Alive · 2010-10-23 00:28:36

Thanks bobbym, but it's impossible for me to get the correct question, I guess next time I will write down the questions neatly and don't postpone it

bobbym · 2010-10-23 00:38:48

Sorry, I could not do more.

Bob · 2010-10-23 03:15:12

Hi Alive,

This is what I think you've asked:

The depth of water d metres in a river, at a time t hours after 12 noon is given by d(t) = 5cos(πt / 12)
[π is pi]

a) sketch the graph of d(t) against t, showing one cycle on the axes, clearly marking in suitable areas

b) state the period and amplitude of depth of water

c) State the highest level of water and the time of day when this occurs

d) State the lowest level of water and time of day when this occurs

e) by solving an appropriate trigonometric equation, find time of day when level of water in river is equal to 2.5 metres

bobbym's graph in post 12 is the right shape. The Cosine graph starts with t = 0, cos(o) = 1, so d = 5x1=5

If the formula has a pi in it then one cycle is over when you get to cos(2pi) [360 degrees but your problem is in radians]

So t x pi / 12 = 2 pi => t / 12 = 2 => t = 24.

So the complete cycle should have d back at 5 when t = 24 not 30. Tides are not exactly repeated after 24 hours but near enough for a mathematical model. (see graph below)

b) So the period is 24 hours and the water level goes from +5 to -5 => amplitude = 5

c) That'll be 5 metres then at t = 0, so at noon.

d) That'll be - 5 metres? I don't know how a river manages this. I wonder if that's why you had a stray 400 in your post.
But it'll happen at t = 12 so at midnight.

Should it have been 400 + 5cos(πt / 12)
in which case the maximum is 405 and the minimum is 395.

e) But now I cannot do this with the 400 in there so I'll go back to the original

5cos(πt / 12) = 2.5 => cos (nt/12) = 0.5

this would be 60 degrees which is pi/3 in radians => pi t /12 = pi /3 => t = 4 ... 4.00 pm.

I did the graph below using Excel. I've left the formula for d in the shot so you can re-create it if you have the software.

Hope that helps. ps. What exam is this for? it looks like an Edexcel AS or higher level GCSE ??

If the latter, I have past papers so I could look it up.

Bob

Last edited by Bob (2010-10-23 03:47:34)

Alive · 2010-10-24 19:38:49

Thanks for the great help there!

Now I really need to know how to do these kinds of graphs.. I need tutorials or worksheets showing how to do it step by step. Do you know any?

bobbym · 2010-10-24 21:28:25

Hi Alive;

There are two good ones at the bottom. Please read them and come back with some questions.

Yes, I think I will give you a problem! Graph y = 2x + 6.

Make a little table by putting in values of x. When x = 0 the above equation becomes y = 2*0 + 6 so y is 6.
We have our first point so put it into the table.

y | 6
------------------------------
x | 0

When x = 1 the above equation becomes y = 2*1 + 6 so y is 8.
We have another point so put it into the table.

y | 6 8
------------------------------
x | 0 2

When x = 2 the above equation becomes y = 2*2 + 6 so y is 10.
We have another point so put it into the table.

y | 6 8 10
------------------------------
x | 0 1 2

Now we have 3 points called coordinates (0,6) (1,2) (2,10). The first number in each pair is the x value and the second number is the y value.

Go here and you will be able to plot them and learn some more.

http://www.mathsisfun.com/data/cartesia … nates.html

And here:

http://www.mathsisfun.com/data/straight_line_graph.html

Play the coordinate game.

http://www.mathsisfun.com/data/click-coordinate.html

Bob · 2010-10-25 07:51:59

hi Alive,

My graph was done in MS Excel. Have you got this software? If so I can take you through a series of trig graphs where you can vary the values and so get the feel for how these graphs behave.

Bob

Alive · 2010-10-25 17:37:29

I understand how to plot the basic graphs. But I don't know how to do sine cosine graphs.. Like
5cos(πt / 12).. and then they keep changing the equation so it looks different adding new things. I don't know how to do these kinds of curves? I don't understand what steps we do to draw it. (amplitude.. period etc..)

And yes I do have excel

bobbym · 2010-10-26 02:10:26

Hi Alive;

I graph the trigonometric ones in the same way that I do simple ones by making a table. I do not have much experience with Excel or any other spreadsheet so bob bundy is your man for that.

You seemed to be doing fine with amplitude and period in the other post.

Bob · 2010-10-26 07:39:28

hi Alive,

I'm in France at the moment and using the hotel wifi. Don't know when I'll be back on so apologies if there's a long wait before the next post.

I'll start with a basic cosine curve. Try it just to iron out any bugs with using Excel for this. It's not the best software for trig graphs but I thought there would be a good chance you'd have it which means we have got a starting point. Anyhow, you only want it so you can understand how the graphs behave; and it'll be good for that.

Excel assumes your angles are in Radians so I've kept with that. If you want a degrees version you'll have to convert the degrees by x pi / 180 before applying the COS function.

Pi is stored in Excel as if it was a function. The code to get it is PI()

To make my graph I let Excel work out the value of pi/6 (30 degrees) and then used formulas to calculate subsequent angles in equal steps.

To 'insert' the graph choose a scatter graph. That might seem a bit odd but the reason is that Excel makes unwelcome assumptions if you ask for a 'line graph' so you don't get sensible x and y coordinates.

To add a line between points use 'Add a Trendline'. Again, Excel hasn't got what we'd like as the types of line don't cover trig functions. I found the best fit is to choose 'polynomial' with the 'order' set to 6 (max possible on my version of Excel)

The picture below shows the values I used and also the formulas so you should be able to reproduce these for a basic cosine curve.

I've just checked what the post looks like and see I haven't included the column and row in the shot to save space. To help you locate which cells .... the zero rads value is in cell D3.

I'll sign off with that; let me know how it goes. I'll start work offline for a more advanced general version.

Bob

Last edited by Bob (2010-10-26 07:46:12)

Bob · 2010-10-26 08:19:44

hi Alive,

It didn't take too long to make a general version so I thought I'd post straight away.

The shot below shows the graph y = 2(cos(0.5x))

2 is called the amplitude and 0.5 the frequency. You can also feed in different phase values. In the example I've kept it at zero.

In general this version will produce graphs of the form y = amplitude x cosine(frequency times 'x' + phase)

You change the amplitude by changing the value in cell D2; the frequency by changing H2 and the phase by changing K2.

The formula in cell D5 picks up these changes to vary the value of y. I then copied that formula into the rest of the row 5 cells.

Note about relative and absolute cell references in formulas.

Normally when you copy a formula into a new cell, Excel makes a relative copy. Thus = COS(D4) becomes = COS(E4) then =COS(F4) and so on as this is copied across. Excel automatically advances the letter from D to E to F and so on.

But for this graph I don't want the cells D2, H2 and K2 to advance in this way otherwise the right amplitude, frequency and phase will not be picked up. Excel allows the user to force absolute references (always pick this cell when copying) by putting a $ symbol in front of the row or column.

Hopefully that made sense; in which case so will the formula for D5

=$D$2*COS($H$2*D4+$K$2)

If not, just copy it exactly and it'll do the job anyway!

You'll have to rescale as you vary the amplitude.

Try a phase angle of =PI()/6 (30 degrees) to start with so you can see what happens for different phase angles.

Frequency is the least satisfactory to show with Excel as the trendline doesn't follow the points well for freq = 2 for example. But it should give you the idea.

Hope that helps.

Bob

Last edited by Bob (2010-10-26 08:22:05)

Math Is Fun Forum

#1 2010-10-22 21:14:13

Need this question answered a.s.a.p

#2 2010-10-22 21:23:16

Re: Need this question answered a.s.a.p

#3 2010-10-22 22:17:15

Re: Need this question answered a.s.a.p

#4 2010-10-22 22:19:41

Re: Need this question answered a.s.a.p

#5 2010-10-22 23:27:46

Re: Need this question answered a.s.a.p

#6 2010-10-22 23:30:00

Re: Need this question answered a.s.a.p

#7 2010-10-22 23:43:53

Re: Need this question answered a.s.a.p

#8 2010-10-22 23:46:57

Re: Need this question answered a.s.a.p

#9 2010-10-22 23:54:41

Re: Need this question answered a.s.a.p

#10 2010-10-22 23:59:48

Re: Need this question answered a.s.a.p

#11 2010-10-23 00:00:10

Re: Need this question answered a.s.a.p

#12 2010-10-23 00:13:30

Re: Need this question answered a.s.a.p

#13 2010-10-23 00:21:45

Re: Need this question answered a.s.a.p

#14 2010-10-23 00:25:14

Re: Need this question answered a.s.a.p

#15 2010-10-23 00:28:36

Re: Need this question answered a.s.a.p

#16 2010-10-23 00:38:48

Re: Need this question answered a.s.a.p

#17 2010-10-23 03:15:12

Re: Need this question answered a.s.a.p

#18 2010-10-24 19:38:49

Re: Need this question answered a.s.a.p

#19 2010-10-24 21:28:25

Re: Need this question answered a.s.a.p

#20 2010-10-25 07:51:59

Re: Need this question answered a.s.a.p

#21 2010-10-25 17:37:29

Re: Need this question answered a.s.a.p

#22 2010-10-26 02:10:26

Re: Need this question answered a.s.a.p

#23 2010-10-26 07:39:28

Re: Need this question answered a.s.a.p

#24 2010-10-26 08:19:44

Re: Need this question answered a.s.a.p

Board footer