OCR January 2006 C3 q9 part iii

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  1. munky90's Avatar
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    OCR January 2006 C3 q9 part iii
    Hey. I got really unstuck with this question so please could someone give me some help?

    9,iii) Solve, for 0<B<90, the equation 3 sin{6\beta}cosec{2\beta} = 4

    I managed to get down to 9 sin{2\beta} - 12 sin^3{2\beta} and earlier in the question I had to prove that sin{3\theta} = 3sin{\theta} - 4sin^3{\theta}

    it might be clearer if you see the paper here

    Thanks in advance

    -Nathe
  2. EierVonSatan's Avatar
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    Re: OCR January 2006 C3 q9 part iii
    9 sin 2B - 12 sin^3 2B = 3(sin 2B -4sin^3 2B) = 3 sin 6B
  3. munky90's Avatar
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    Re: OCR January 2006 C3 q9 part iii
    I tried that. You end up with

    sin{6\beta} = \frac{4}{3}

    The mark scheme said something about attempting to find a non zero value for sin2B?
  4. EierVonSatan's Avatar
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    Re: OCR January 2006 C3 q9 part iii
    3(sin 2B -4sin^3 2B)cosec 2B = 3 (1 - 4sin^2 2B)

    divided by sin 2B, so you have to solve sin 2B = 0 also
  5. munky90's Avatar
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    Re: OCR January 2006 C3 q9 part iii
    Ah, ok, brilliant. Thanks a lot.
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