Maths C3 - Trigonometry... Help??

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    (Original post by RDKGames)
    No need, the quadratic is all in terms of a single unknown variable and that's as simple as it gets.
    OMG, I actually got it

    Thank you thank you thank you thank you thank you

    So happy!!
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    (Original post by Philip-flop)
    OMG, I actually got it

    Thank you thank you thank you thank you thank you

    So happy!!
    No problem, well done.
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    How have I been stuck on Chapter 6: Trigonometry of the Edexcel C3 Modular Maths Textbook for so long? Feel's like it's taking me ages to get through the book I was hoping to have finished all of it by now!
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    (Original post by Philip-flop)
    How have I been stuck on Chapter 6: Trigonometry of the Edexcel C3 Modular Maths Textbook for so long? Feel's like it's taking me ages to get through the book I was hoping to have finished all of it by now!
    Anything particular that you're stuck on?
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    (Original post by RDKGames)
    Anything particular that you're stuck on?
    Practically everything! :P

    I'm constantly asking for help and still make stupid little mistakes. Feel like I have no hope of succeeding at A2 Barely even succeeded at AS!!

    Feel like I need a tutor but really can't afford it :/
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    (Original post by Philip-flop)
    Practically everything! :P

    I'm constantly asking for help and still make stupid little mistakes. Feel like I have no hope of succeeding at A2 Barely even succeeded at AS!!
    Just practice otherwise you'll carry those stupid little mistakes to the exam which is not what you want.
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    (Original post by RDKGames)
    Just practice otherwise you'll carry those stupid little mistakes to the exam which is not what you want.
    Yeah true. But sometimes I feel like I'm practicing loads and loads but still struggle later on :/

    How do I make sure I don't lose motivation?
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    (Original post by Philip-flop)
    Yeah true. But sometimes I feel like I'm practicing loads and loads but still struggle later on :/

    How do I make sure I don't lose motivation?
    Er, dunno. If I don't succeed in one question, I learn from it, and take on then next one because I want to get it right, I suppose. Exams are still a loooong way away so you'll get it by then.
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    (Original post by RDKGames)
    Er, dunno. If I don't succeed in one question, I learn from it, and take on then next one because I want to get it right, I suppose. Exams are still a loooong way away so you'll get it by then.
    Yeah, I guess I've just got to keep powering my way through and learn from my mistakes. But I seem to struggle to get the answer in the first place unless you're there prompting me like you have been

    That's true, exams are a long way away, but in terms of the time that I have, I don't actually have a lot of study time
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    Ok so I'm stuck on Example 13 from chapter 6 of the Edexcel C3 Modular Maths Textbook part (a) ... For now :P ... Anyway I have a lot of questions to ask about this so if anyone could help I'd be more than thankful

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    1) What gives the impression that ...  \mathrm{cosec}^4 \theta - \cot ^4 \theta is the difference of two squares??

    2) With this situation how do you find the difference of two squares, as I only know how to when an equation is in the form Ax^2-b

    3) How/where is the identity 1+\cot ^2 \theta = \mathrm{cosec}^2 \theta is being used??


    Again, sorry for the ridiculously silly questions :/
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    (Original post by Philip-flop)
    Ok so I'm stuck on Example 13 from chapter 6 of the Edexcel C3 Modular Maths Textbook part (a) ... For now :P ... Anyway I have a lot of questions to ask about this so if anyone could help I'd be more than thankful


    1) What gives the impression that ...  \mathrm{cosec}^4 \theta - \cot ^4 \theta is the difference of two squares??

    2) With this situation how do you find the difference of two squares, as I only know how to when an equation is in the form Ax^2-b

    3) How/where is the identity 1+\cot ^2 \theta = \mathrm{cosec}^2 \theta is being used??


    Again, sorry for the ridiculously silly questions :/
    1) Because both terms have the same even power and the whole expression is a difference. For any even power you can factor out a 2 which would make some arbitrary term to the power of 2, ie a square. So something like a^6=(a^3)^2 which is a square of some term to the third power.

    2) \mathrm{cosec^4 \theta} - \mathrm{cot^4 \theta} = (\mathrm{cosec^2 \theta})^2-(\mathrm{cot^2 \theta})^2=...

    Also Ax^2-b is not a form for a difference of two squares.. Difference of two squares is a^2-b^2=(a+b)(a-b). So something like A^2x^2-b^2 would indeed be a difference of two squares because A^2x^2=(Ax)^2

    3) Second line. Second bracket equals 1.
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    (Original post by Philip-flop)
    Ok so I'm stuck on Example 13 from chapter 6 of the Edexcel C3 Modular Maths Textbook part (a) ... For now :P ... Anyway I have a lot of questions to ask about this so if anyone could help I'd be more than thankful


    1) What gives the impression that ...  \mathrm{cosec}^4 \theta - \cot ^4 \theta is the difference of two squares??

    2) With this situation how do you find the difference of two squares, as I only know how to when an equation is in the form Ax^2-b

    3) How/where is the identity 1+\cot ^2 \theta = \mathrm{cosec}^2 \theta is being used??
    A difference of two squares is this: a^2 - b^2 = (a-b)(a+b).

    Here you have (\csc^2 \theta)^2 - (\cot^2 \theta)^2  = (\csc^2 \theta - \cot^2 \theta)(\csc^2 \thetaa + \cot^2 \theta).

    Now the first bracket is \csc^2 \theta - \cot^2 \theta but from your identity you know that \csc^2 \theta = \cot^2 \theta + 1 so subtracting \cot^2 from both sides, we have \csc^2 \theta - \cot^2 \theta = 1.

    So your factorisation becomes (1)(\csc^2 \theta + \cot^2 \theta)
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    (Original post by RDKGames)
    3) Second line. Second bracket equals 0.
    ..
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    (Original post by Zacken)
    ..
    lol...
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    (Original post by RDKGames)
    1) Because both terms have the same even power and the whole expression is a difference. For any even power you can factor out a 2 which would make some arbitrary term to the power of 2, ie a square. So something like a^6=(a^3)^2 which is a square of some term to the third power.

    2) \mathrm{cosec^4 \theta} - \mathrm{cot^4 \theta} = (\mathrm{cosec^2 \theta})^2-(\mathrm{cot^2 \theta})^2=... try this.

    Also Ax-b is not a form for a difference of two squares.. Difference of two squares is a^2-b^2=(a+b)(a-b)

    3) Second line. Second bracket equals 1.
    Oh yeah. The difference of two squares never really made perfect sense to me until now. Thank you! I only knew how to solve the difference of two squares if it was written for example as... x^2-4 = (x+2)(x-2) but that's as basic as I could work out

    (Original post by Zacken)
    A difference of two squares is this: a^2 - b^2 = (a-b)(a+b).

    Here you have (\csc^2 \theta)^2 - (\cot^2 \theta)^2  = (\csc^2 \theta - \cot^2 \theta)(\csc^2 \thetaa + \cot^2 \theta).

    Now the first bracket is \csc^2 \theta - \cot^2 \theta but from your identity you know that \csc^2 \theta = \cot^2 \theta + 1 so subtracting \cot^2 from both sides, we have \csc^2 \theta - \cot^2 \theta = 1.

    So your factorisation becomes (1)(\csc^2 \theta + \cot^2 \theta)
    Thank you!!! That step by step process has really helped me!! These new Trig Identities that are introduced in C3 are really intimidating but I'm glad you're there to help I just need to keep familiarising myself. Hopefully it won't be too much of a struggle :doh:
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    I can't help but keep you the good work mate. Oh and I can't help because I am learning C3 now
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    Trying to understand how for part (b) that...
    sin^2 \theta +tan^2 \theta <<<goes from...
    ...to this... (1-cos^2 \theta)+(\sec ^2 \theta -1)


    Edit: False alarm, I was being stupid. I realised that I just had to re-arrange using Trig Identities
    Edit: False alarm, I was being stupid. I realised that I just had to re-arrange using Trig Identities

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    Edit: False alarm, I was being stupid. I realised that I just had to re-arrange using Trig Identities
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    (Original post by Philip-flop)
    Trying to understand how for part (b) that...
    sin^2 \theta +tan^2 \theta <<<goes from...
    ...to this... (1-cos^2 \theta)+(\sec ^2 \theta -1)
    Because
    \cos^2 \theta + \sin^2 \theta \equiv 1

    and (from dividing both sides by cos squared)

    1+\tan^2 \theta \equiv \sec^2 \theta

    Rearrange for sine squared, and tan squared, then sub them in.
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    (Original post by RDKGames)
    Because
    \cos^2 \theta + \sin^2 \theta \equiv 1

    and (from dividing both sides by cos squared)

    1+\tan^2 \theta \equiv \sec^2 \theta

    Rearrange for cos squared, and tan squared, then sub it in.
    Thank you. I think all these Trig Identities are making me lose my mind which is why I've been making silly mistakes like that!
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    (Original post by Philip-flop)
    Thank you. I think all these Trig Identities are making me lose my mind which is why I've been making silly mistakes like that!
    As long as you remember \sin^2 \theta + \cos^2 \theta \equiv 1 you can pretty much derive the rest from it so you don't necessarily have to remember all of them.
 
 
 
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