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    Hi

    I've just been doing Chapter 16 in Edexcel C2,Trig,and it's proving to be a bit of a struggle...

    The equations are okay,save a few,but what I'm really confused about is how to get all the angles within a given range.

    For example,how would I go about solving something like:

    (2sinx)^2 -sinx - 1=0 where x is equal to or greater than 0 and equal to or less than 360.

    Also,if anyone has ANY tips or tricks on how to get all the angles in a given range,please do share them!

    Thanks a lot
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    Have you been taught the general solutions for sin, cos, and tan? You can obtain the angles in any range with these.
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    When you have trig. equations with cosines and sines, and cosine squared and sine squared and such, usually a good tactic is to get the whole thing in terms of the same trig ratio and then solve it as a quadratic

    Spoiler:
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    eg. Solve:  \sin x - \cos^2 x + 1 = 0 \ \mathrm{between} \ 0 < x < 360

     \implies \sin x - (1-\sin^2 x) + 1 = 0

     \implies \sin x + \sin^2 x = 0

     \implies \sin x(\sin x+1) =0

     \mathrm{Solving} \ \sin x = 0 \ \mathrm{gives} \ \boxed{x = 180} \ \mathrm{in \ the \ range}

     \mathrm{Solving} \ \sin x+1 = 0 \ \mathrm{gives} \ \boxed{x = 270} \ \mathrm{in \ the \ range}


    In your question, you already have it all in terms of sine.

    So we have  4\sin^2 x - \sin x - 1 = 0

    If we let  \sin x = m notice that the problem becomes  4m^2 - m -1 =0 which you should be able to solve.

    When you have tans mixed in there, using the fact that  \tan x = \dfrac{\sin x}{\cos x} usually comes in handy.

    Spoiler:
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    eg.1. Solve  \tan x + \cos x = 0 \ \mathrm{between} \ 0 < x < 360

     \implies \dfrac{\sin x}{\cos x} + \cos x = 0

     \implies \sin x + \cos^2 x = 0

     \implies \sin x + 1 - \sin^2 x = 0

     \implies \sin^2 x - \sin x -1 =0

    Let  \sin x = u

     \implies u^2 - u -1 = 0

     \implies u = \dfrac{1\pm \sqrt{1+4}}{2} = \frac{1\pm \sqrt{5}}{2}

     \implies \boxed{\sin x = \dfrac{1\pm \sqrt{5}}{2}} which can then be solved.

    eg.2. Solve  \sin x = \cos x \ \mathrm{between} \ 0 < x < 360

     \implies \dfrac{\sin x}{\cos x} = 1

     \implies \tan x = 1

     \implies \boxed{x = 45, \ 135}


    Hope this helps.
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    (Original post by EierVonSatan)
    Have you been taught the general solutions for sin, cos, and tan? You can obtain the angles in any range with these.
    Hmm,I'm not quite sure what you mean by those,maybe I've been taught them but we just use a different terminology to refer to them...would you mind expanding on that?

    Thanks for the quick reply!
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    1. Factorise it.
    2. Find what the possible solutions are
    3. So now you got 2sinx = ......., work it out.
    4. Use a CAST diagram or a graph to find all the solutions within a given interval.
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    (Original post by SyedT)
    Hmm,I'm not quite sure what you mean by those,maybe I've been taught them but we just use a different terminology to refer to them...would you mind expanding on that?

    Thanks for the quick reply!
    As in these: http://mathsfirst.massey.ac.nz/Trig/TrigGenSol.htm
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    (Original post by EierVonSatan)
    As in these: http://mathsfirst.massey.ac.nz/Trig/TrigGenSol.htm
    Looking at that,I haven't been taught it yet...is it like a formula to get the angles in any range,and do you think it'd be worth me learning them?
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    (Original post by SyedT)
    Looking at that,I haven't been taught it yet...is it like a formula to get the angles in any range,and do you think it'd be worth me learning them?
    Well it's the way I've always done them, but some people use the CAST method - it's upto you really
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    (Original post by EierVonSatan)
    Well it's the way I've always done them, but some people use the CAST method - it's upto you really
    Well I've used the CAST method so far...but sometimes I don't manage to get enough answers,e.g when I reached the end of a question and solved the final equation:

    (tanx)^2=3/4 I got x=40.9 and 220.9,but there are four solutions,and I'm not quite sure how to get there...
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    (Original post by SyedT)
    Well I've used the CAST method so far...but sometimes I don't manage to get enough answers,e.g when I reached the end of a question and solved the final equation:

    (tanx)^2=3/4 I got x=40.9 and 220.9,but there are four solutions,and I'm not quite sure how to get there...
    Then the graph would get you those
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    (Original post by Andylol)
    Then the graph would get you those
    I did realise that,but in the exam it wouldn't be the most sensible thing to do,drawing the graph,and also,I'm not terribly good at imagining the tan graph in my head :redface:
 
 
 
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