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    (Original post by Emz)
    Hi, hope someone can help me again! This question is on the exam style paper in the back of the P3 revision book, its question 3.

    A circle has equation x² + y² - 8x + 2y + 8 = 0

    Point C on the circle is the nearest point to the origin,O.
    Find the distance between O and C.

    So far I've worked out the centre and radius of the circle and tried drawing a diagram to help me but I can't quite see what to do.

    Emma x x x
    Hint (quite a big one)...

    The line between the origin and the centre will have the point C on it. If you calculate the equation of this line then you will know the line and (due to the fact that you know the radius) you will know how far along the line point C is.
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    (Original post by Leekey)
    Hint (quite a big one)...

    The line between the origin and the centre will have the point C on it. If you calculate the equation of this line then you will know the line and (due to the fact that you know the radius) you will know how far along the line point C is.
    How about working the equation of the line from the centre of the circle to the origin, and solving it by substituting it into the original cartesian equation?
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    (8/17, -2/17) ?
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    (Original post by Bhaal85)
    (8/17, -2/17) ?
    If it's wrong, I have hayfever.
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    If that makes the distance OC root17 - 3 then its right, I've given up on P3 for a bit, I'll have another go later. Thanks for all your help though!

    Emma x x x
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    Man, I wish I had this thread last year.
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    (Original post by Bhaal85)

    cos(A+B) = cosAcosB-SinASinB
    cos(A-B) = cosAcosB+SinASinB
    Sin(A+B) = SinACosB+CosASinB
    Sin(A-B) = SinACosB-CosACosB
    Tan(A+B) = (TanA+TanB)/(1-TanATanB)
    Tan(A-B) = (TanA-TanB)/(1+TanATanB)
    When do we actually need to use those? I remember there was this question which involved sin3x or something which needed those identities...but I can't quite figure out what it was :confused:
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    (Original post by kenkennykenken)
    When do we actually need to use those? I remember there was this question which involved sin3x or something which needed those identities...but I can't quite figure out what it was :confused:
    sin3x diff = 3cosx
    integrate = -cos3x / 3

    i dont need we need those!
    bt
    tan^2x +1 =sec^2
    cos2x = cos ^2x - sin 2 ^x
    r really important
    the rest u can figure out when doing the question!
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    (Original post by tammypotato)
    sin3x diff = 3cosx
    You wanna take a 2nd look at that?
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    ah ok...thats alright then...because ive never had to use those identities and was wondering when i would need them. phew!
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    (Original post by Leekey)
    You wanna take a 2nd look at that?
    lol 3cos3x sorry
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    (Original post by kenkennykenken)
    When do we actually need to use those? I remember there was this question which involved sin3x or something which needed those identities...but I can't quite figure out what it was :confused:
    Prove:

    Sin(x+45)-cos(x+45)=√2sinx and hence express sin15 in surd form.
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    (Original post by Bhaal85)
    Prove:

    Sin(x+45)-cos(x+45)=√2sinx and hence express sin15 in surd form.
    bt they r in the formula book so no need to learn em by heart!
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    am i weird:

    i never learnt the eqution of integration n differentiation by part n when i luk at them i dont understand n gt really confused
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    I ain't too great on this subject either:

    ∫udv/dx dx = uv - ∫vdu/dx

    Basically i think there is one rule for lnx and the rest applies to all

    Inx

    If the integral contains lnx make that equal to u. If thats so, then the v value is always the integrated version of whatever the product to it is.

    For example:

    ∫x²lnx dx

    lnx = u x² = dv/dx
    1/x = du/dx 1/3x³ = v

    so putting these into the formula: the answer is

    ∫x²lnxdx = lnx . 1/3x³ - ∫1/3x³ .1/x

    = 1/3x³lnx - 1/9x³ + c

    The difference between lnx and the other functions are that we do not yet know how to integrate lnx.

    Non lnx cases (everything else)

    The same as above but it does not matter which is v or u, i suggest the dv/dx value to be the trigonometric functions, as i believe that is easier to deal with.

    For example

    ∫xsin2x dx

    u = x du/dx = 1
    dv/dx = -1/2cos2x v = sin2x

    so putting these into the formula.

    ∫xsin2x = x . -1/2cos2x - ∫-1/2cos2x .1

    = -1/2xcos2x + 1/4sin2x + c

    I think thats basically all you need to do.

    This page on mathsnet should be able to help you understand if need be:

    http://www.mathsnet.net/asa2/modules/p35parts.html

    Hope this helps.
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    I learn the formula for integrating two products as:

    ∫vdu/dx dx = uv - ∫udv/dx

    sorry for being dense, but is this the same? as

    ∫udv/dx dx = uv - ∫vdu/dx?
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    I wouldn't like to bet on it but i see no problem with it, until some brainbox proves me rong haha
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    (Original post by ResidentEvil)
    I learn the formula for integrating two products as:

    ∫vdu/dx dx = uv - ∫udv/dx

    sorry for being dense, but is this the same? as

    ∫udv/dx dx = uv - ∫vdu/dx?
    Yep its exactly the same

    I hate integration by substitution :mad:
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    There's vector A and vector B, and you can work out the line AB. If D is a point on line AB, how do i find the position vector of D such that OD is perpendicular to AB? I don't know how to apply dot product here as I don't know anything about D...
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    Well the direction vector of D is AB i think
 
 
 
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