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    5 (i)Express 3 sinθ + 2cosθ in the form Rsin(θ + α), where R > 0 and 0◦ < α < 90◦. [3]

    (ii) Hence solve the equation 3 sinθ + 2cosθ = 7
    2, giving all solutions for which 0◦ < θ < 360◦. [5]

    stuck on these two. I knew how to do them just need some guidance as I have forgotten.

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    Rsin(a+b)= Rsin(a).cos(b)+Rcos(a).sin(b)

    now 'compare' 3sinθ+2cosθ to Rsin(a).cos(b)+Rcos(a).sin(b).

    can remember where to go from here?
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    3sin\theta + 2cos\theta = Rsin(\theta+\alpha) = Rsin\theta cos\alpha + Rsin\alpha cos\theta
    To work out R, you take the coefficients of sin and cos:
    R = \sqrt{3^2+2^2}
    Then you take the sin or cos side from the top equation:
    2cos\theta = Rsin\alpha cos\theta
    Divide through:
    2 = Rsin\alpha
    Which lets you work out \alpha

    Quote me if you don't understand or have more questions.
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    Rsin(Theta + Alpha) = Rsin(theta)cos(alpha) + R Sin(alpha)Cos(Theta)

    therefore Rcos(alpha = 3 and R sinalpha = 2

    R= square root of 2^2 +3^2

    Then divide so you have cos(alpha) and then cos^-1 that to get alpha
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    Just wondering once you have a value for alpha do you take the full value to put it back into the sin(x+alpha) or would you use the say 2 decimal place value of of?

    i know how to do it all im just unsure how accurate you have to be with the decimals
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    All the questions I've come across from past papers tell you the degree of accuracy to use, normally 3 dp or 3sf

    If you can't see any choose 3sf or, to be safe, don't round your answer
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    Got it now guys I forgot the R bit
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    (Original post by Snapshot13)
    Just wondering once you have a value for alpha do you take the full value to put it back into the sin(x+alpha) or would you use the say 2 decimal place value of of?

    i know how to do it all im just unsure how accurate you have to be with the decimals
    what the guy above said, but make sure you look at what the question says regarding the value of alpha, for example here it says 0◦ < α < 90◦, if it's like 0 < α < 2pi then leave the value in terms of pi, not degrees.
 
 
 
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Updated: January 19, 2010

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