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Circular Functions

  1. Jan 16, 2010 #1
    the equation 3sinx - 1 = b, where b is a positive real number, has one solution in the interval (0,2pi). The value of b is:

    Frankly I have no idea where to even start with this problem.
     
  2. jcsd
  3. Jan 16, 2010 #2

    tiny-tim

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    Hi TyErd! :smile:

    (have a pi: π :wink:)

    Hint: how many solutions in (0,2π) does 3sinx - 1 = 15 have?

    And 3sinx - 1 = 0.5 ? :wink:
     
  4. Jan 16, 2010 #3
    Um. thnx for the pi. How do you know how many solutions there are?
     
  5. Jan 16, 2010 #4

    tiny-tim

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    Draw a graph and find out.

    Get on with it!
     
  6. Jan 16, 2010 #5
    alright i've drawn the graph, so what parts of the graph do i have to look at to know how many solutions there?
     
  7. Jan 16, 2010 #6
    hm..
     
  8. Jan 16, 2010 #7

    Mentallic

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    Which parts? Umm...

    If I asked you to find out how many solutions there are to [itex]x^2=10[/itex] how would you go about doing that by looking at a graph?
     
  9. Jan 16, 2010 #8

    Mark44

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    And you should be looking only at the part of the graph on the interval [0, 2π].
     
  10. Jan 16, 2010 #9

    tiny-tim

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    Nooo … (0,2π). :wink:
     
  11. Jan 16, 2010 #10

    Mark44

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    Right, tiny-tim. I missed that it was the open interval.
     
  12. Jan 16, 2010 #11
    so when it says solutions, should i be looking at the x intercepts?
     
  13. Jan 16, 2010 #12

    Mark44

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    What is the graph that you have drawn? Specifically, what is the formula of the function you have graphed?
     
  14. Jan 16, 2010 #13
    I tried to draw 3sinx-1=15 by taking 15 onto the other side but i've just realised that isnt right. How do you graph an equation that equals a number?
     
  15. Jan 16, 2010 #14

    Mentallic

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    Graph [itex]15=3sinx-1[/itex]
    Then graph [itex]y=15[/itex]

    Do you see how if you tried to solve these two equations simultaneously, you would get [itex]15=3sinx-1[/itex]?

    Are there any intersections between the two functions?

    Now, can you find any number b (such as 15) that makes it such that the equation [itex]3sinx-1=b[/itex] has only 1 real solution in the interval between 0 and 2π?
    This is the same as saying for what number b will the function [itex]y=b[/itex] intersect the function [itex]y=3sinx-1[/itex] only once in the interval [itex](0,2\pi)[/itex]?
     
  16. Jan 16, 2010 #15
    Thankyouuu! i get it finally, you made it so much easier. thnx
     
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