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Math Help - trigo again

  1. #1
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    trigo again

    Find the minimum value of the following expression and the value of x between 0 and 360 when the minimum occurs .

    3 cos 2x + sin 2x --- this is the expression


    3 cos 2x + sin 2x = r cos(2x-a)

     r=\sqrt{10}

    tan a=1/3 , a =18.43

    When minimum occurs , \sqrt{10}cos(2x-18.43)=-\sqrt{10}

    cos(2x-18.43)=-1

    2x-18.43=180 or 2x-18.43=270

    Then i get my 2 values of x from there .

    But i am wrong . Where is my mistake >?
    Last edited by thereddevils; August 4th 2009 at 05:40 AM.
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  2. #2
    Senior Member apcalculus's Avatar
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    Quote Originally Posted by thereddevils View Post
    Find the minimum value of the following expression and the value of x between 0 and 360 when the minimum occurs .

    3 cos 2x + sin 2x = r cos(2x-a)

     r=\sqrt{10}

    tan a=1/3 , a =18.43

    When minimum occurs , \sqrt{10}cos(2x-18.43)=-\sqrt{10}

    cos(2x-18.43)=-1

    2x-18.43=180 or 2x-18.43=270

    Then i get my 2 values of x from there .

    But i am wrong . Where is my mistake >?

    Which expression are you trying to optimize? You have posted an equation with two expressions, one on each side.
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  3. #3
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    I have not looked at the first part of your work, but this caught my eye:
    cos(2x-18.43)=-1

    2x-18.43=180 or 2x-18.43=270
    That should be 540, not 270. The minimum values of the cosine function occur at odd multiples of 180.

    Now, although we have the restriction 0^{\circ} \le x < 360^{\circ}, you have a 2x, which means that 0^{\circ} \le 2x <\; {\color{red}720}^{\circ}. That's why the 2nd number above should be 540.


    01
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  4. #4
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    Quote Originally Posted by apcalculus View Post
    Which expression are you trying to optimize? You have posted an equation with two expressions, one on each side.

    edited
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  5. #5
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    Quote Originally Posted by yeongil View Post
    I have not looked at the first part of your work, but this caught my eye:

    That should be 540, not 270. The minimum values of the cosine function occur at odd multiples of 180.

    Now, although we have the restriction 0^{\circ} \le x < 360^{\circ}, you have a 2x, which means that 0^{\circ} \le 2x <\; {\color{red}720}^{\circ}. That's why the 2nd number above should be 540.


    01

    thanks .. i should hv noticed that ....
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