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Trouble simplifying

  1. Apr 27, 2007 #1
    1. The problem statement, all variables and given/known data
    I am reviewing some old exam solutions and came across something I cannot figure out. I'm don't understand how they simplify from the first equation to the second. I looked up a table of trig identies but could not find anything that would help.


    2. Relevant equations
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    3. The attempt at a solution
     
  2. jcsd
  3. Apr 27, 2007 #2

    Gib Z

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    Homework Helper

    Expand cos ( theta + pi/4), and times it by root 2.
     
  4. Apr 28, 2007 #3

    HallsofIvy

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    The relevant trig identity is [itex]cos(\theta+ \phi)= cos(\theta)cos(\phi)- sin(\theta)sin(\phi)[/itex]

    Ignoring the 'm(t)' which just "goes along for the ride", you have [itex]2cos(\theta)- 2 sin(\theta)[/itex]. Obviously, since 2> 1, there is no [itex]\phi[/itex] that has both sine and cosine equal to 2- you will need divide by something. But you would still have [itex]cos(\phi)= sin(\phi)[/itex]. What value of [itex]\phi[/itex] has that property? And what do you then need to divide by?
     
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