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anonymous

  • 5 years ago

if trying to find all solutions on the interval 0,2pi sin2x=sinx so x=1/2? or how do i solve?

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  1. myininaya
    • 5 years ago
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    sin2x=2sinxcosx so 2sinxcosx=sinx 2sinxcosx-sinx=0 sinx(2cosx-1)=0 sinx=0 and 2cosx-1=0

  2. myininaya
    • 5 years ago
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    lets solve sinx=0 first

  3. myininaya
    • 5 years ago
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    what x makes sinx zero

  4. myininaya
    • 5 years ago
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    think about your unit circle

  5. myininaya
    • 5 years ago
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    sin(0) is what?

  6. anonymous
    • 5 years ago
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    0 or pi

  7. myininaya
    • 5 years ago
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    sin(0)=0 sin(2pi)=0 so x=0 and 2pi now we have the other equation 2cosx-1=0 => cosx=1/2

  8. myininaya
    • 5 years ago
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    what can plug in where the x is that give you 1/2 (we are looking at the equation cosx=1/2)

  9. anonymous
    • 5 years ago
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    60 degrees

  10. anonymous
    • 5 years ago
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    the other btw was 0 degrees or 180 degrees for sin

  11. myininaya
    • 5 years ago
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    oh yes and pi very good for the first

  12. anonymous
    • 5 years ago
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    so answeres are 0,1/2,pi?

  13. myininaya
    • 5 years ago
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    so 60 degrees and what else for this equation equation

  14. myininaya
    • 5 years ago
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    no not 1/2

  15. myininaya
    • 5 years ago
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    60 degrees or pi/3 there is also another one for the second equation

  16. anonymous
    • 5 years ago
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    ah

  17. anonymous
    • 5 years ago
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    0,pi/3,pi that seems like all we can get i think cause thats both sin and hte one cos

  18. anonymous
    • 5 years ago
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    @myininaya: Congrats for the new title. I was you 100th fan by the way :D

  19. anonymous
    • 5 years ago
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    i was 99th XD

  20. myininaya
    • 5 years ago
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    thanks lol

  21. myininaya
    • 5 years ago
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    so anyways what is cos(300 degrees)

  22. anonymous
    • 5 years ago
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    10pi/6

  23. myininaya
    • 5 years ago
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    no maybe it will help if i wrote it in radians what is cos(5pi/3)

  24. anonymous
    • 5 years ago
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    isnt that the same just reduced?

  25. myininaya
    • 5 years ago
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    ok 10pi/6=5pi/3 but what is cos(5pi/3)

  26. myininaya
    • 5 years ago
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    =1/2

  27. anonymous
    • 5 years ago
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    -1/2?

  28. anonymous
    • 5 years ago
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    isnt it - cause bottom right quadrent?

  29. anonymous
    • 5 years ago
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    nvm cos is x so positive if on right side

  30. myininaya
    • 5 years ago
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    k :) so the solutions to sinx=0 in the interval [0,2pi] are 0,pi,2pi and the solutions to cosx=1/2 in the interval [0,2pi] are pi/3, 5pi/3

  31. myininaya
    • 5 years ago
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    you have 5 solutions in all

  32. anonymous
    • 5 years ago
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    thank you

  33. myininaya
    • 5 years ago
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    np

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