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anonymous

  • 5 years ago

Help with Trig-- sin X + 2 sin X cos X= 0 solve for all possible radian solutions (please explain each step) Thank you

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  1. amistre64
    • 5 years ago
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    do you know your trig identities?

  2. anonymous
    • 5 years ago
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    yes, 2 sin x cos x = sin 2A

  3. amistre64
    • 5 years ago
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    good, then when does sin(x) + sin(2x) = 0? recall also that " -sin(x) = sin(-x)" that might be useful

  4. amistre64
    • 5 years ago
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    sin(2x) = -sin(x) sin(2x) = sin(-x) 2x = -x 2x + x = 0 3x = 0 .... when x = 0 thats what I come up with as a solution....

  5. amistre64
    • 5 years ago
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    0 and pi i believe are the answers

  6. anonymous
    • 5 years ago
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    thats what I got as an answer, but the answers in the back of the textbook says differently : pi k, 2 pi/3 +2 pi k, 4 pi/3 +2pi k

  7. amistre64
    • 5 years ago
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    ahhh.... ALL possible solutions involves an interger constant of "k"

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  8. amistre64
    • 5 years ago
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    there do appear to be 3 spots between 0 and 2pi that match up...

  9. anonymous
    • 5 years ago
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    ohhhh

  10. anonymous
    • 5 years ago
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    i see it, but i dont understand

  11. anonymous
    • 5 years ago
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    how to get the points without knowing it

  12. amistre64
    • 5 years ago
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    ...yeah, trig is highly visual.

  13. amistre64
    • 5 years ago
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    we could try this: sin(x) + 2 sin(x) cos(x)= 0 sin(x)(1 + 2cos(x)) = 0

  14. amistre64
    • 5 years ago
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    sin(x) = 0 is a solution and (1+2cos(x)) = 0 are solutions

  15. amistre64
    • 5 years ago
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    1+ 2 cos(x) = 0 2cos(x) = -1 cos(x) = -1/2

  16. amistre64
    • 5 years ago
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    that works better :)

  17. amistre64
    • 5 years ago
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    0, pi for sin(x) cos(x) is negative in Q2 and Q3...

  18. amistre64
    • 5 years ago
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    cos(pi/3) = 1/2 .... 60 degrees. that would make it 120 degrees and 240 degrees as well.

  19. amistre64
    • 5 years ago
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    2pi/3 + k2pi and 4pi/3 + k2pi...right?

  20. anonymous
    • 5 years ago
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    yes, thank you very much!... I can see a light at the end of the tunnel!!! thank you

  21. amistre64
    • 5 years ago
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    :) all it takes is a little persistents and alot of luck lol

  22. anonymous
    • 5 years ago
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    thank you, your right about that!!

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