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

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

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)

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

2. Originally Posted by mattmati
Hopefully in proper section.
Yes; trigonometry questions go in the trigonometry section.

Originally Posted by mattmati
The graph shows output model of vibrations of engine, and can be expressed function;

x(t)=(cosπt)(sin20πt)

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
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!

3. 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
To solve 1s part I know I should use radians in my calculation but dunno how to even start it.

4. Originally Posted by mattmati
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)

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
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.

5. 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

6. Hi Guys, I too am struggling with the same problem.

7. Originally Posted by gtchucker09
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
When does a product of 2 functions equal 0?

8. Originally Posted by lev888
When does a product of 2 functions equal 0?
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.

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