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Math Help - Trigonometric Equation

  1. #1
    Newbie
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    Sep 2008
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    Trigonometric Equation

    Hi again x.x

    I'm having a huge problem with these, here goes:

    It is given that a=2sinθ + cosθ and b=2cosθ + sinθ where
    0 θ 360

    (i) Show that a
    + b is constant for all values of θ
    (ii) Given that 2a = 3b show that tanθ = 4/7 and find the corresponding values of θ

    My answer for (i): 5sin
    θ + 5cosθ = θ by adding A and B squared.

    For (ii) I don't understand the question.

    Also, could someone point me to a website containing detailed explainations and examples of these? I feel like I only half understand them :/

    Thanks again guys
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  2. #2
    Super Member Matt Westwood's Avatar
    Joined
    Jul 2008
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    Reading, UK
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    You've been given a and b, so you can construct 2a and 3b and see what the equation gives you:

    2 (2 \sin \theta + \cos \theta) = 3 (2 \cos \theta + \sin \theta)

    simplifying that down you get:

    4 \sin \theta + 2 \cos \theta = 6 \cos \theta + 3 \sin \theta

    4 \sin \theta - 3 \sin \theta = 6 \cos \theta - 2 \cos \theta

    \sin \theta  = 4 \cos \theta

    \frac {\sin \theta}{\cos \theta} = \tan \theta  = 4

    ... which is not the answer I was expecting, I was expecting it to be 4/7.


    Did you copy the question right?
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  3. #3
    Newbie
    Joined
    Sep 2008
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    a=2sinθ + cosθ and b=2cosθ + sinθ

    No indeed .. *
    b=2cosθ - sinθ

    It works out perfectly when you change the sign >.o
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