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Thread: Help with year 11 Trig 3 unit

  1. #1
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    Aug 2016
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    Help with year 11 Trig 3 unit

    Can anyone please help me answer these two questions. I only managed to get half the working out right.

    I attached the questions below


  2. #2
    Loquacious One
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    Feb 2009
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    Re: Help with year 11 Trig 3 unit

    I recall doing the 2nd question late last year.

    The basic idea is very simple. Say if you draw a right-angled triangle ABC, right-angled at B, with hypotenuse of length 7 say, then the 2 shorter sides are AB = 7 cos A and BC = 7 sin A.

    Now for this question, form the 3 right angled triangles with hypotenuses AP, PQ and QR (each of length x, say) resp., with their shorter sides parallel to, and vertical to side AB respectively. Also drop the perpendicular to line AB from R, meeting AB at Z say.

    Then tan(angle BAR) = RZ/AZ

    Now RZ is the sum of the vertcal sides of the 3-right angled triangles, and
    AZ is the sum of the 3 horizontal sides. Therefore:

    RZ = x sin @ + x sin 2@ + x sin 3@ = x (sin@ + sin 2@ + sin 3@)

    AZ = xcos @ + x cos 2@ + x cos 3@ = x (cos @ + cos 2@ + cos 3@)

    Hence the result.
    Last edited by Drongoski; 18 Apr 2017 at 11:54 PM.
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