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    Okay, let's say I have two equations:

    5 = Rcos\alpha, 6 = Rsin\alpha

    I know to work out the value of R, you square the equations, then add them, as follows:

    25 = R^2cos^2\alpha, 36 = R^2sin^2\alpha
    25 + 36 = R^2(cos^2\alpha +sin^2\alpha) = R^2
    \therefore R = \sqrt{61}

    But what I don't understand is, if I go down a different route (which should still work) I get a different answer:

    Add both equations:

    5 + 6 = Rsin\alpha + Rcos\alpha - nothing wrong with that right? Now if squared it just like that, it would be fine. But if I actually find the sum of 5 and 6, then square it, it goes weird:

    11 = Rsin\alpha + Rcos\alpha
    121 = R^2
    R = 11

    What am I doing which is 'nonsensical'? From my point of view, I can't see anything that I have done wrong, but I end up with the wrong answer >< .
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    Squaring the RHS side would give  (Rsina + Rcosa)^2 not  R^2
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    You left out the "2R(sin a + cos a)" when squaring
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    (Original post by ViralRiver)
    Okay, let's say I have two equations:

    5 = Rcos\alpha, 6 = Rsin\alpha

    I know to work out the value of R, you square the equations, then add them, as follows:

    25 = R^2cos^2\alpha, 36 = R^2sin^2\alpha
    25 + 36 = R^2(cos^2\alpha +sin^2\alpha) = R^2
    \therefore R = \sqrt{61}

    But what I don't understand is, if I go down a different route (which should still work) I get a different answer:

    Add both equations:

    5 + 6 = Rsin\alpha + Rcos\alpha - nothing wrong with that right? Now if squared it just like that, it would be fine. But if I actually find the sum of 5 and 6, then square it, it goes weird:

    11 = Rsin\alpha + Rcos\alpha
    121 = R^2
    R = 11

    What am I doing which is 'nonsensical'? From my point of view, I can't see anything that I have done wrong, but I end up with the wrong answer >< .
    Remember

     (Rsin\alpha + Rcos\alpha)^2 = R^2sin^2\alpha +2R^2sin\alpha cos\alpha + R^2cos^2\alpha = R^2(sin^2\alpha + cos^2\alpha) + 2R^2sin\alpha cos\alpha = R^2 + 2R^2sin\alpha cos\alpha

    hope i helped
    Good Luck in your C3 exam!
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    Ahh okay. Just to make sure, since it seems I've been fooled by my teachers. if x=a+b, then does x^2=a^2+b^2 or x^2=(a+b)^2? I've always been taught the former (i.e square everything individually) but I've always thought it was the latter >< .
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    (Original post by ViralRiver)
    x^2=(a+b)^2
    This is correct. NEVER ever do the first one.
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    Thanks. I hate my GCSE teacher xD .
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    I did it by solving them as simultaneous equations:

    \displaystyle\frac{Rsin\alpha}{R  cos\alpha} = \displaystyle\frac{6}{5}



tan\alpha = \displaystyle\frac{6}{5}

    therefore  \alpha = 50.2\degree


    R = \displaystyle\frac{5}{cos50.2} = \sqrt{61}
 
 
 
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