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How is sin teta = 0?

  1. Nov 21, 2016 #1
    1. The problem statement, all variables and given/known data
    IMG-1479738683063-V_01.jpg
    IMG-1479738706327-V_01_01.jpg
    2. Relevant equations


    3. The attempt at a solution
    The first picture is the question
    The second picture is the marking scheme
    I have circled in yellow the problem
    I would like to know how sin teta = 0
    Thank you
     
  2. jcsd
  3. Nov 21, 2016 #2

    PeroK

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    What don't you understand about it?
     
  4. Nov 21, 2016 #3
    I do know how cos teta = 1/3
    But the sin teta part I don't get I couldn't transpose the formula 3sin teta = sin teta / cos teta to sin teta = 0
    So I know I m missing something fundamental
     
  5. Nov 21, 2016 #4

    PeroK

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    What is ##\tan(0)##?

    What is ##3\sin(0)##?
     
  6. Nov 21, 2016 #5
    Both is 0
     
  7. Nov 21, 2016 #6

    PeroK

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    So, ##\theta = 0## is a solution to your equation ##\tan \theta = 3\sin \theta##.

    What about other values of ##\theta## where ##\sin \theta = 0##?
     
  8. Nov 21, 2016 #7
    Hmmm I guess I know what your saying
    Teta= 180
    That part I understand
    Thank you very much
     
  9. Nov 21, 2016 #8

    Ray Vickson

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    The book's explanation is poorly worded; it should have said ##\cos(\theta) = 1/3## OR ##\sin(\theta) = 0##. That means that one or the other of those two possibilities can occur, and that corresponds to the existence of more than one solution to the problem in the interval ##0^o < \theta < 360^o##.

    If you plot the graphs of ##y = 3\sin(\theta)## and ##y = \tan(\theta)## over the interval ##0^o < \theta < 360^o##, you will see that there are three points where the two graphs cross (five points of crossing if you include ##\theta = 0^o## and ##\theta =360^o##). The equation ##\sin(\theta) = 0## has one solution in ##(0^0,360^o)##, while the equation ##\cos(\theta) = 1/3## has two solutions in ##(0^o,360^o)##.
     
  10. Nov 21, 2016 #9
    This is from an alevel past paper
    But this explanation is very nice
    Thank you very much
     
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