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Help explain an easy question

  1. Oct 2, 2007 #1
    For the problem sin-(1/sqrt2) ...(sin-.. being arcsin) the answer is pi/4 but is that the only answer becuase pi/4 lies between [-90,90]???

    or would it also be right to say PI-4PI=3pi/4? (although i think this is wrong)
  2. jcsd
  3. Oct 2, 2007 #2


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    Do you know what the graph of sin(x) looks like? It goes up from (0,0) to ([itex]\pi/2[/itex], 1) then back down to ([itex]\pi[/itex],0). You are right that sin([itex]3\pi /4) is also equal to [itex]\sqrt{2}{2}[/itex] but IF YOUR PROBLEM SPECIFIES THAT THE ANSWER MUST BE BETWEEN [itex]-\pi /2[/itex] to [itex]\pi/2[/itex]. If it does not then [itex]3\pi /4[/itex] is the "principal" value (it's the value your calculator gives you) so if you are asking that "tan-1" be a single valued function, that would be its value. If you are solving "tan(x)= [itex]\sqrt{2}/2[/itex]" then there are an infinite number of solutions- rhe two you give plus any multiple of 2 [itex]\pi[/itex].
  4. Oct 2, 2007 #3
    No the problem does not give the intervals of [-90,90]...just the question... so i can come to the conclusion that 3pi/4 is also correct (as is pi/4)
  5. Oct 2, 2007 #4
    Halls.. My calculator gives me the answer of pi/4 though not 3pi/4 and where does the sqrt of 22 come from?
  6. Oct 3, 2007 #5


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    My "tex" messed up. It should have been [itex]\sqrt{2}/2[/itex].
    Also the [itex]3\pi /4[/itex] was just a typo on my part. I meant, of course, [itex]\pi/4[/itex].
    By the way- it is really bad practice to talk about "intervals [-90,90]" AND give values in terms of [itex]\pi[/itex]. You are going to have to choose whether you are working in degrees or radians! (I strongly recommend radians.)

    Again, if your problem is to find all solutions to [itex]sin(x)= \sqrt{2}/2[/itex], then the solutions are all numbers of the form [itex]\pi/4 + 2n\pi[/itex] and [itex]3\pi/4+ 2n\pi[/itex] where n is any integer. If your problem is to find [itex]Sin^{-1}(\sqrt{2}/2)[/itex] with arcsine as a single-valued function, then the only answer is [itex]\pi/4[/itex]. (Notice the capital "S" on "Sin-1". Many texts use the capital when they want to mean the single-valued function: the principal value.)
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