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Is sin(x + y) = 1 a function of x on R?

  1. Mar 22, 2014 #1
    Is "sin(x + y) = 1" a function of x on R?

    1. The problem statement, all variables and given/known data

    Determine if the following relation is a function of [itex]x[/itex] on [itex]\mathbb R[/itex]:

    [tex]sin(x + y)=1[/tex]

    3. The attempt at a solution

    Rearrange to make [itex]y[/itex] the subject:

    [tex]y = sin^{-1}(1) - x[/tex]

    Then, I simply calculated some points and plotted a graph, which was linear. The points I used:

    (-3, 4.57)
    (-2, 3.57)
    (-1, 2.57)
    (0, 1.57)
    (1, 0.57)
    (2, -0.43)
    (3, -1.43)
    (4, -2.43)

    As you can see, this would produce a linear graph with a gradient of [itex]m = 1[/itex]; however, the solution that has been given states that this is not a function, because for all [itex]x\in\mathbb R[/itex] there exist infinitely many [itex]y[/itex] values.

    Appreciate any help in explaining why this is so, as I am stumped :)

    Thanks in advance.
     
  2. jcsd
  3. Mar 22, 2014 #2

    SammyS

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    For how many values of θ is sin(θ) = 1 ?
     
  4. Mar 22, 2014 #3

    LCKurtz

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    Or, to elaborate on SammyS's question, if ##x=0## can you find more than one ##y## that works?
     
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