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    Hey guyss, there's a question that comes up in almost ALL C3 edexcel papers and I just don't understand how to do them, could i pleaseee have some help! This is one example of the question:

    a) Show that cos2X+sin2X can be written in the form Rsin(2X+a).
    b) hence, solve, in the interval 0<X<180, the equation cos2X+sin2X=1, giving your answers as rational multiples of pie.

    (this question is Also number 9 in the C3 edexcel book, page 112)

    I can do part (a), but i cannot do part (b), pleasee can somebody tell me how! Thanks so much.
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    (Original post by inspiration9)
    Hey guyss, there's a question that comes up in almost ALL C3 edexcel papers and I just don't understand how to do them, could i pleaseee have some help! This is one example of the question:

    a) Show that cos2X+sin2X can be written in the form Rsin(2X+a).
    b) hence, solve, in the interval 0<X<180, the equation cos2X+sin2X=1, giving your answers as rational multiples of pie.

    (this question is Also number 9 in the C3 edexcel book, page 112)

    I can do part (a), but i cannot do part (b), pleasee can somebody tell me how! Thanks so much.

    you can do Rsin(2x+a)=1
    Then sin(2x+a)=1/R
    Then 2x+a=arcsin(1/R)

    ...

    see if you can get it now!
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    what did you get for a? subsitute 2x+a=u and solve it like sinu=1/R and do siin inverse and substitute your values into 2x+a and find x
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    (Original post by thebassking)
    you can do Rsin(2x+a)=1
    Then sin(2x+a)=1/R
    Then 2x+a=arcsin(1/R)

    ...

    see if you can get it now!
    Thankss, I can get up to there, the bit I have trouble with is using the quadrants and trying to work out what answers you get! It doesn't seem to make sense!
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    (Original post by inspiration9)
    Thankss, I can get up to there, the bit I have trouble with is using the quadrants and trying to work out what answers you get! It doesn't seem to make sense!
    what initial value of x do you get, if you dont know how to convert it to within the region look at a sin graph and use that to compare it to the x value you get.
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    (Original post by thebassking)
    what initial value of x do you get, if you dont know how to convert it to within the region look at a sin graph and use that to compare it to the x value you get.
    The equation i get is:
    √2sin(2X+ 0.785) = 1

    So then I end up with:
    2X+0.785=0.785

    Their answers are 0,45,180,225 (degrees) and that is the bit i dont understand, how from the previous step, you get to the answers!:confused:
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    (Original post by inspiration9)
    Thankss, I can get up to there, the bit I have trouble with is using the quadrants and trying to work out what answers you get! It doesn't seem to make sense!
    for sin the solutions will be pie-(the answer you obtain) and also adding and subtrating 360. do these methods within the range they ask for. is that what you meant ?
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    (Original post by inspiration9)
    The equation i get is:
    √2sin(2X+ 0.785) = 1

    So then I end up with:
    2X+0.785=0.785

    Their answers are 0,45,180,225 (degrees) and that is the bit i dont understand, how from the previous step, you get to the answers!:confused:
    edit sorry i didnt read you post properly, give me a sec
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    (Original post by lethal786)
    for sin the solutions will be pie-(the answer you obtain) and also adding and subtrating 360. do these methods within the range they ask for. is that what you meant ?
    Ye thats what I thought, But in this example, could you please show me how that works. :o:
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    (Original post by inspiration9)
    Hey guyss, there's a question that comes up in almost ALL C3 edexcel papers and I just don't understand how to do them, could i pleaseee have some help! This is one example of the question:

    a) Show that cos2X+sin2X can be written in the form Rsin(2X+a).
    b) hence, solve, in the interval 0<X<180, the equation cos2X+sin2X=1, giving your answers as rational multiples of pie.

    (this question is Also number 9 in the C3 edexcel book, page 112)

    I can do part (a), but i cannot do part (b), pleasee can somebody tell me how! Thanks so much.
    cos2X+sin2X=1
    i.e. Rsin(2X+a) = 1

    sin(2x+a)= 1/R

    Now, since you found the values of R and a you can change the domain of the function. ( remember when you took it in C2 last year?)

    let 2x+a = y [ 2(0)+a <y< 2(180)+a]
    Siny = 1/R

    calculate the values of y. and then find then in terms of x. (x= (y-a)/2)

    When you calculate the values of y add 360 to each answer and see if what you get is still inside the domain.
 
 
 
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