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anonymous

  • 4 years ago

Can anyone help me with sin(x)+sin(5x)=2?

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  1. anonymous
    • 4 years ago
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    what is the maximum of sin(x)?

  2. anonymous
    • 4 years ago
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    The max for sin(x) = 1 so the only way the equation can equal 2 is for sin(x) and sin(5x) = 1.

  3. anonymous
    • 4 years ago
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    Ok, but is there a way to solve it when not using a deductive method?

  4. anonymous
    • 4 years ago
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    The value for x for sin(x) = 1 would be pi/2 in radians or 90 degrees. Therefore the value of sin(5*pi/2) also equal one and the sum equals two.

  5. anonymous
    • 4 years ago
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    I think you could use the identity \[\sin \alpha + \sin \beta = 2\sin0.5(\alpha+\beta)\cos0.5(\alpha+\beta)\] and then set this equal to two. This would give you \[\sin0.5(\alpha+\beta)\cos0.5(\alpha+\beta)\] = 1

  6. anonymous
    • 4 years ago
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    there are many correct values of x: pi/2, -pi/2, 3pi/2, etc etc

  7. anonymous
    • 4 years ago
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    Correct values are (pi/2)+2 k pi.

  8. anonymous
    • 4 years ago
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    @commdoc Typo: you mean sin(A) + sin(B) = 2sin((A+B)/2)cos((A-B)/2)

  9. anonymous
    • 4 years ago
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    k is integer.

  10. anonymous
    • 4 years ago
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    Thanks anyway.

  11. anonymous
    • 4 years ago
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    yes - anytime sin(x) is not 1, you cannot get a solution. anytime sin(x) = 1, then sin(5x) = 1 as well, so you get a solution whenever sin(x)=1.

  12. anonymous
    • 4 years ago
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    yeah thanks BF

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