Find values on x axis above function: x(t)=(cosπt)(sin20πt)

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mattmati

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Hi. First post on forum. Hopefully in proper section. I have a question like this;


The graph shows output model of vibrations of engine, and can be expressed function;

[FONT=&quot] x(t)=(cos[/FONT][FONT=&quot]π[/FONT][FONT=&quot]t)(sin20[/FONT][FONT=&quot]π[/FONT][FONT=&quot]t) [/FONT]

t194_tma03_17j_q02_f01.eps.jpg
For what values of t in interval 0-1 the amplitude x(t) is zero? Hint; evaluate sin nπ for integer values of n
 
mattmati said:
Hopefully in proper section.
Click to expand...
Yes; trigonometry questions go in the trigonometry section. :p

mattmati said:
The graph shows output model of vibrations of engine, and can be expressed function;

x(t)=(cosπt)(sin20πt)

View attachment 9210
For what values of t in interval 0-1 the amplitude x(t) is zero? Hint; evaluate sin nπ for integer values of n
Click to expand...
We'll be glad to help, but first we'll need to know where you're having trouble. So please reply with a clear listing of your thoughts and efforts so far, starting with the "Hint" they gave you. Thank you! ;-)
 
Be honest I dont even know how to start it. Apparentaly I skipped smth in previous chapters of my study.
There is 2nd part of question to find derivative which I did using product rule , and result was
f’(t)= cosπt*20πcos20πt- πsinπt*sin20πt
Click to expand...
To solve 1s part I know I should use radians in my calculation but dunno how to even start it.
 
mattmati said:
Hi. First post on forum. Hopefully in proper section. I have a question like this;


The graph shows output model of vibrations of engine, and can be expressed function;

x(t)=(cosπt)(sin20πt)

View attachment 9210
For what values of t in interval 0-1 the amplitude x(t) is zero? Hint; evaluate sin nπ for integer values of n
Click to expand...
So x(t) is a product (of (cosπt) and (sin20πt) ) and it equals 0. Hmmm, when does a product = 0????
Where can you go with this hint? Please show us your work.
 
Hi Guys, Not trying to hijack the thread but I too have to face the same problem.

I have used desmos to plot the function and as I move along the x axis I notice that the curve intercepts the x axis every increment of 0.05.

So for the question of 'What values of t in the interval t=0 to t=1 is the amplitude of x (t) zero?' I guess the answer is 0.05, 0.1, 0.15 ... etc all the way to 1?

If this is the case then I need to prove this by doing something with the function. The Hint 'evaluate sin n pi for integer values of n what is the value of the cosine?' doesn't really mean much to me

I have been told to look where the sin and cos have zero values then equate the values in the brackets and find an expression for t.

I feel like it will be completely obvious if someone shows me what to do so can someone please give me a gentle nudge in the right direction by giving me a hint and then I can go away and carry on trying to solve this?

many thanks
 
gtchucker09 said:
If this is the case then I need to prove this by doing something with the function. The Hint 'evaluate sin n pi for integer values of n what is the value of the cosine?' doesn't really mean much to me
Click to expand...

When does a product of 2 functions equal 0?
 
lev888 said:
When does a product of 2 functions equal 0?
Click to expand...

when 1 of the factors is equal to 0.

I have looked at this possibility...

sin(20*pi*n) I can get this to equal 0 at every increment of 0.05 i.e. 0, 0.05, 0.10, 0.15 so surely thats the answer?

my tutor has recommended I look for where the sin and cos have zero values and then equate the values in the brackets to find an expression for t.

He also said:

  1. How does the function x(t) equal zero? What must happen to the cosine and/or sine functions to make this equal to zero?
  2. When does the cosine function equal zero?
  3. What value would you then have for t (as the cosine function can equal zero on more than one occasion so there is scope for using the letter for an integer, n, which may be odd or even?)
  4. When does the sine function equal zero?
  5. Again, with the integer n, (odd or even, or for all values of n) what value would t equal?

I can only answer as follows: 1 - the sin or cos must be equal to 0. as mentioned above. 2 - the cosine function equals 0 when the number ends in .5 i.e. 1.5, 2.5 etc. 3 - no idea on this. 4 - sin function equals 0 when the value of t is 0.05, 0.10 0.15 or any number that follows this series. 5 - no idea on this.

can anyone nudge me in the right direction please.
 
I also am very stuck with this question anyone get it in the end. I was like you just plugging numbers in and getting some results but have no idea how to set my answer out

please help

thanks loooperb
 
does anyone know what the method is called in math books

does anyone know what the method is called in math books, its a real mixture of everything.

I really need help with this
 
gtchucker09 said:
Hi Guys, Not trying to hijack the thread but I too have to face the same problem.

I have used desmos to plot the function and as I move along the x axis I notice that the curve intercepts the x axis every increment of 0.05.

So for the question of 'What values of t in the interval t=0 to t=1 is the amplitude of x (t) zero?' I guess the answer is 0.05, 0.1, 0.15 ... etc all the way to 1?

If this is the case then I need to prove this by doing something with the function. The Hint 'evaluate sin n pi for integer values of n what is the value of the cosine?' doesn't really mean much to me

I have been told to look where the sin and cos have zero values then equate the values in the brackets and find an expression for t.

I feel like it will be completely obvious if someone shows me what to do so can someone please give me a gentle nudge in the right direction by giving me a hint and then I can go away and carry on trying to solve this?

many thanks
Click to expand...

for what angle(s) is sin=0?
cos?
 
loooperb said:
does anyone know what the method is called in math books, its a real mixture of everything.

I really need help with this
Click to expand...
It is a mixture of stuff? You have a product for x(t) and you want to know when it equals 0. Answer: When one of the factors equals 0. This was given in at least two earlier posts.

Since we want x(t) = cos(nt) * sin(20nt) = 0, it follows that either cos(nt) = 0 or sin(20nt) = 0.

Now sin (q) = 0 when q= +/- 0, = +/- pi, +/- 2pt, +/- 3pi, ...

But your angle was not q. Regardless of what we name the angle it can only equal +/- 0pi, = +/- pi, +/- 2pi, +/- 3pi, ...

Now n is an integer so 20nt is short hand for +/-20t (when n=+/-10), +/- 40t (when n = +/-2), +/- 60t... . What do YOU think t can be so that

+/-20t (when n=+/-10), +/- 40t (when n = +/-2), +/- 60t... will be in +/- 0pi, = +/- pi, +/- 2pi, +/- 3pi, ... ?

There will be many solutions for t, now pick one that is in [0,1].


Do the same for cos(nt) = 0
 
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