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lgbasallote

  • 2 years ago

Find all values of x such that \(\sin 2x = \sin x\) and 0 < x < 2\(\pi\)

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  1. lgbasallote
    • 2 years ago
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    i suppose the only way for this to happen is if the x were 0....

  2. JamesWolf
    • 2 years ago
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    yeah or pi, but you specified x < 2pi

  3. lgbasallote
    • 2 years ago
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    hmm i suppose pi works

  4. lgbasallote
    • 2 years ago
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    sin 2x = sin x arcsin both sides 2x = x 2x - x = 0 x = 0 how can i get the other values?

  5. JamesWolf
    • 2 years ago
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    hmmm good question

  6. leedomathgeek
    • 2 years ago
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    sin(2x)=2sin(x)cos(x) Therefore, sin(2x)=sin(x) --> 2sin(x)cos(x)=sin(x) 2sin(x)cos(x)-sin(x)=0 sin(x)[2cos(x)-1]=0 Now either sin(x)=0 ---> x=0,pi,... or 2cos(x)-1=0 --> cos(x)=1/2 ---> x=pi/3

  7. lgbasallote
    • 2 years ago
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    then i suppose the others can be solved by adding pi?

  8. leedomathgeek
    • 2 years ago
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    Why do you want to add a pi?

  9. lgbasallote
    • 2 years ago
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    because one angle is missing

  10. leedomathgeek
    • 2 years ago
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    You have only 3 solutions

  11. leedomathgeek
    • 2 years ago
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    0, pi/3, pi

  12. lgbasallote
    • 2 years ago
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    there's actually 5.. but i know how to get one of the missing angles...

  13. leedomathgeek
    • 2 years ago
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    oh ya i though x between 0 and pi

  14. leedomathgeek
    • 2 years ago
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    sure 2pi is the 4th solution

  15. lgbasallote
    • 2 years ago
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    yes

  16. leedomathgeek
    • 2 years ago
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    and x=2pi-p/3=5pi/3

  17. leedomathgeek
    • 2 years ago
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    is the 5th solution

  18. lgbasallote
    • 2 years ago
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    oh subtract pi/3 from 2pi...ah yes... the negative angle

  19. leedomathgeek
    • 2 years ago
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    exactly ...since cos(x) is positive in the 4th quad

  20. apple_pi
    • 2 years ago
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    Here's an example you might want to look at: tan(4x) = -tan(2x) 0° ≤ x ≤ 360° tan(4x) = tan(-2x) ****DONT DO THIS: 4x = -2x INSTEAD... 4x = 180n -2x (Write one side as a general solution) then simplify: 6x = 180n x = 30n then you have all possible values of x now find all the ones that work, and you have all solutions

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