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    Are there certain angles I need to know? I'm freaking out about this exam seriously. For example I just did a question, and I had to give my answer in terms of pye (sp?!?)

    And I got to a stage where I knew that Cos(theta)= 0.5

    And the answer is pye/3....

    how am I supposed to know that arccos 0.5 = pye/3?

    Am i missing something... :s
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    sin30 & cos60=1/2
    sin45 & cos45=1/root(2)
    sin60 & cos30=root(3)/2
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    The Greek letter \pi is called "pi", although I don't suppose it matters.

    You're supposed to know for C2, let alone C3, the values of \sin x, \cos x, \tan x when x = 0, \frac{\pi}{6}, \frac{\pi}{4}, \frac{\pi}{3}, \frac{\pi}{2}, \pi and also the rules that determine the values given other multiples of these, like -\frac{\pi}{2} and \frac{3\pi}{4}.

    For example, if you know that \sin \frac{\pi}{4} = \frac{1}{\sqrt{2}} then you'll know that if \sin \theta = \frac{1}{\sqrt{2}} then \theta = \frac{\pi}{4} is a solution.
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    (Original post by nuodai)
    The Greek letter \pi is called "pi", although I don't suppose it matters.

    You're supposed to know for C2, let alone C3, the values of \sin x, \cos x, \tan x when x = 0, \frac{\pi}{6}, \frac{\pi}{4}, \frac{\pi}{3}, \frac{\pi}{2}, \pi and also the rules that determine the values given other multiples of these, like -\frac{\pi}{2} and \frac{3\pi}{4}.

    For example, if you know that \sin \frac{\pi}{4} = \frac{1}{\sqrt{2}} then you'll know that if \sin \theta = \frac{1}{\sqrt{2}} then \theta = \frac{\pi}{4} is a solution.
    Okay that's great thanks, but i still don't understand how I'm supposed to know the answer to the question I asked, you know... how i know that arccos 0.5 = pi/3?


    And I knewwww that pye didn't look right thanks
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    I never bothered to learn them. It's just supposed to be quicker than having to type them into your calculator.
    It's made no difference to how well I've done, don't worry about it.
    The only time you'd really have to know them is in a non-calculator paper, but I don't think they do non-calcs with trig in.
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    (Original post by maxfire)
    I never bothered to learn them. It's just supposed to be quicker than having to type them into your calculator.
    It's made no difference to how well I've done, don't worry about it.
    The only time you'd really have to know them is in a non-calculator paper, but I don't think they do non-calcs with trig in.
    oh great, thats really helpful thanks bit of relief...
    Could you help me with this then, how would you solve it

    Cos(theta)= 0.5

    And the answer is pi/3....

    how am I supposed to know that arccos 0.5 = pi/3?

    (I have to leave ans in terms of pi)
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    (Original post by irish_4_life)
    oh great, thats really helpful thanks bit of relief...
    Could you help me with this then, how would you solve it

    Cos(theta)= 0.5

    And the answer is pi/3....

    how am I supposed to know that arccos 0.5 = pi/3?

    (I have to leave ans in terms of pi)
    If you know that \cos \frac{\pi}{3} = \frac{1}{2} then you should see the \frac{1}{2} and recognise that \theta = \frac{\pi}{3} makes the LHS match up with the RHS. That is, if you know that \cos \frac{\pi}{3} = \frac{1}{2} then you know that \frac{\pi}{3} = \arccos \frac{1}{2}.
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    (Original post by nuodai)
    If you know that \cos \frac{\pi}{3} = \frac{1}{2} then you should see the \frac{1}{2} and recognise that \theta = \frac{\pi}{3} makes the LHS match up with the RHS. That is, if you know that \cos \frac{\pi}{3} = \frac{1}{2} then you know that \frac{\pi}{3} = \arccos \frac{1}{2}.
    thanks, but is there a way I can work it out wthout knowing all the special angles, like is there a method to work it out....

    My exam is this week, I have an awful teacher and two more exams between now and then :/
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    (Original post by irish_4_life)
    thanks, but is there a way I can work it out wthout knowing all the special angles, like is there a method to work it out....

    My exam is this week, I have an awful teacher and two more exams between now and then :/
    Well you could draw a graph, but that more or less requires you to know the values. They're part of the syllabus so you should really know them.
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    (Original post by irish_4_life)
    thanks, but is there a way I can work it out wthout knowing all the special angles, like is there a method to work it out....

    My exam is this week, I have an awful teacher and two more exams between now and then :/
    yes. draw an equilateral triangle with length 2, split it down the middle to get two right-angle triangles and see what you get

    although really, just use your calculator
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    if you know roughly the common ones that come up, you can just use them on your calculator...like try diving by root3, or pi, and see if it comes up with a nice fraction, like 1/2. (can't actually remember which trig function gives that, but that's all i do)
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    It helps to remember that pi radians is 180 degrees. If you know these values in degrees, which is IMO simpler than trying to learn the values in radians, you can simply divide by 180 and multiply by pi.
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    okay so say im to learn all of these 'special angles' where do i find them? because they're not in my c3 book!
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    (Original post by Iota Null)
    It helps to remember that pi radians is 180 degrees. If you know these values in degrees, which is IMO simpler than trying to learn the values in radians, you can simply divide by 180 and multiply by pi.
    Sorry, I dont understamd what this has to do with radians :s
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    (Original post by nuodai)
    Well you could draw a graph, but that more or less requires you to know the values. They're part of the syllabus so you should really know them.
    where can i find them? x
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    (Original post by irish_4_life)
    where can i find them? x
    sin 0 = cos 90 = 0
    sin 30 = cos 60 = 1/2
    sin 45 = cos 45 = √(2)/2
    sin 60 = cos 30 = √(3)/2
    sin 90 = cos 0 = 1
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    (Original post by irish_4_life)
    how am I supposed to know that arccos 0.5 = pye/3?
    Or you could just type cos-1(0.5) into your calculator and if you were in radians mode it would give you \frac{\pi}{3}
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    Use a right angled isoceles triangle and an equilateral triangle to derive them...

    theta (from the first diagram) = 45 or pi/4
    alpha (from the second) = 60 or pi/3
    beta = 30 or pi/6
    Then use SOHCAHTOA.
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    Oh dear, i see a nice C/D coming on on Wednesday if I dont buck up! I just dont understand the concept of these special angles, and what radians have to do with them? Sorry, this is probably tedius fr a lot of you... :/
 
 
 
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