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Math Help - trig, minimum value?

  1. #1
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    trig, minimum value?

    (a) Show that 3sin3θ−4cos3θ can be written in the form Rsin(3θ−α), with R>0 and 0<α<90.

    (b) Deduce the minimum value of 3sin3θ−4cos3θ and work out the smallest positive value of θ (to the nearest 0.1) at which it occurs.

    I did the first part and got  5sin( 3\theta-53.1)

    but how do I find the minimum value? I have set it equal to 0, but that does not give me the correct answer.

    can someone please tell me
    ?

    Thanks!
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  2. #2
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    Quote Originally Posted by Tweety View Post
    (a) Show that 3sin3θ−4cos3θ can be written in the form Rsin(3θ−α), with R>0 and 0<α<90.

    (b) Deduce the minimum value of 3sin3θ−4cos3θ and work out the smallest positive value of θ (to the nearest 0.1) at which it occurs.

    I did the first part and got  5sin( 3\theta-53.1)

    but how do I find the minimum value? I have set it equal to 0, but that does not give me the correct answer.

    can someone please tell me
    ?

    Thanks!
    the minimum value of 5sin(3t - 53.1) is -5 , and occurs when 3t-53.1 = 270 degrees
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