Trigonometric Equations

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  • #1
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Homework Statement



This problem came up while solving a physics problem in waves.
We have the equation cos(96πt)cos(4πt)=0
How many times does the L.H.S. become 0 during the time t=0 to t=1s ?


The Attempt at a Solution



Nothing.
 

Answers and Replies

  • #2
HallsofIvy
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A product of numbers is 0 only if at least one number is 0. cos(x) is 0 when x is an odd multiple of [itex]\pi/2[/itex]. For what values of t is 192t an odd integer? For what values of t is 8t an odd integer?
 
  • #3
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For what values of t is 192t an odd integer?

t can be 1/192, 1/64 and for second case t=1/8 only. But 3 times is not the correct answer.
 
  • #4
HallsofIvy
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I have no idea what you are doing! I get 192/2= 96 values of t so that 192t is an odd integer (so that [itex]cos(96\pi t)= 0[/itex]) and 8/2= 4 values of t so that 8t is an odd integer (and [itex]cos(4\pi t)= 0[/itex]). That gives a total of 90 values of t for which [itex]cos(96\pi t)cos(4\pi t)= 0[/itex].
 
  • #5
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Even I have no idea what you did :biggrin:. Anyway I was wrong earlier.
Why did you divide 192 and 8 by 2? What do we get by doing that?
 
  • #6
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Somebody help me out!!!
 
  • #7
HallsofIvy
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You are looking for t such that 192t is an odd integer. 192t= 1 if t= 1/192, of course, but also, 192t= 3 if t= 3/192, 192t= 5 if t= 5/192, etc. We can do that for every odd integer up to 192- and 192/2 of the integers less than 192 are odd.
 
  • #8
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ohh..its that way!. Sometimes simple things become very complex.
I understood it now. Thank you :smile:
 

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