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Babybee24

cos^2(x)+cos(x)sin(x)=0 solve for x

  • one year ago
  • one year ago

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  1. myininaya
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    Try factoring

    • one year ago
  2. Babybee24
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    I factored a cos(x) out but then im stuck

    • one year ago
  3. myininaya
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    cos(x)( ? + ? ) =0 So what should be in the places of those ?'s once you factor out cos(x)?

    • one year ago
  4. Babybee24
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    cos(x)(cosx+sinx)

    • one year ago
  5. myininaya
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    Yes. Set both factors equal to 0. cos(x)=0 ; cos(x)+sin(x)=0

    • one year ago
  6. myininaya
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    Solve cos(x)=0 for x And find the value x so that cos(x) and sin(x) are opposites (i.e cos(x)=-sin(x))

    • one year ago
  7. Babybee24
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    cosx=pie/2 ?

    • one year ago
  8. myininaya
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    cos(x)=0 for x=pi/2 cos(x) does not equal pi/2 But one value that satisfies cos(x)=0 is x=pi/2 Are there any other values?

    • one year ago
  9. Babybee24
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    x=3pi/2

    • one year ago
  10. myininaya
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    Ok and you can also say we have x=pi/2+2npi where n is an integer or x=3pi/2+2n pi where n is an integer

    • one year ago
  11. myininaya
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    We also need to find the values of x where cos(x) and sin(x) have opposite values.

    • one year ago
  12. myininaya
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    |dw:1357920385873:dw| As you can see they will be opposite in quadrant 2 and 4.

    • one year ago
  13. myininaya
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    |dw:1357920430907:dw| These points is where cos(x) and sin(x) are opposite. Now what angle are these points at from the initial ray?

    • one year ago
  14. Babybee24
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    135 and 315?

    • one year ago
  15. myininaya
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    Correct.

    • one year ago
  16. myininaya
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    Now should your answer be in radians or degrees?

    • one year ago
  17. Babybee24
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    um radians?

    • one year ago
  18. myininaya
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    So 135*pi/180 or 315*pi/180

    • one year ago
  19. myininaya
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    Don't forget we can go around the circle infinitely many times from those angles.

    • one year ago
  20. myininaya
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    So 135pi/180+2npi , 315pi/180+2npi

    • one year ago
  21. myininaya
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    Don't forget the other solutions we wrote above. Good job. :)

    • one year ago
  22. Babybee24
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    thanks!

    • one year ago
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