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hannahg

  • 3 years ago

Find all solutions in the interval [0, 2π). sin2x + sin x = 0

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  1. .Sam.
    • 3 years ago
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    Do you know what's the identity for sin2x?

  2. hannahg
    • 3 years ago
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    noo i forgot..

  3. .Sam.
    • 3 years ago
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    sin2x=2sinxcosx

  4. .Sam.
    • 3 years ago
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    So how do you proceed?

  5. hannahg
    • 3 years ago
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    2sinx+cosx+sinx=0 right? what do i do next?

  6. .Sam.
    • 3 years ago
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    no, it should be from sin2x + sin x = 0 to 2sinxcosx + sin x =0 right?

  7. hannahg
    • 3 years ago
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    ohh yea

  8. .Sam.
    • 3 years ago
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    you should try factoring now

  9. hannahg
    • 3 years ago
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    sinx(2cosx+1)=0 is this right? what do i do next? o.O

  10. AravindG
    • 3 years ago
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    ya u r right :)

  11. .Sam.
    • 3 years ago
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    yes, now you can let sinx=0 and 2cosx+1=0 then find the x values

  12. AravindG
    • 3 years ago
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    equate that to 0 and find x values

  13. hannahg
    • 3 years ago
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    so i got cosx=-1/2 how do i find the value of x?

  14. .Sam.
    • 3 years ago
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    well you can do this cosx=-1/2 x=cos^{-1} (-1/2)

  15. hannahg
    • 3 years ago
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    so what are all possible values of x? 0 and......what else O.o

  16. AravindG
    • 3 years ago
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    @hannahg :) instead of o.O

  17. .Sam.
    • 3 years ago
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    no its not 0

  18. hannahg
    • 3 years ago
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    @AravindG :)

  19. .Sam.
    • 3 years ago
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    you calculate cos^(-1) 1/2 first without minus on half you'll get 60 degrees

  20. hannahg
    • 3 years ago
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    yes:)

  21. .Sam.
    • 3 years ago
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    then use this chart for cosine |dw:1358873950517:dw| we are looking at the minus side since we got minus half. then 180-60=120 degrees 180+60=240 degrees

  22. AravindG
    • 3 years ago
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    @hannahg thats better :)

  23. hannahg
    • 3 years ago
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    yes. so all the possible solutions will be pi, pi/3, 2pi/3?

  24. .Sam.
    • 3 years ago
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    you still have sinx=0 to do

  25. hannahg
    • 3 years ago
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    yes......! so 0?

  26. .Sam.
    • 3 years ago
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    yes but dont forget about 180

  27. .Sam.
    • 3 years ago
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    |dw:1358874634831:dw|

  28. .Sam.
    • 3 years ago
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    since theta is 0, then you get 180

  29. hannahg
    • 3 years ago
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    @.Sam. so what are all solutions in the interval??

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