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    (a) Show that [email protected] = [email protected](16sin^[email protected]^[email protected]+5) done this

    (b) Find exact values of x for 16x^4-20x^2+5=0 done this and got plus or minus sqrt(5/8 + or - sqrt(5)/8) which is correct

    (c) Deduce exact values of sin(pi/5) and sin(2pi/5), explaining clearly the reasons for your answers.

    I'm struggling to make a connection between the earlier parts of the question to do (c). Any hints?
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    Could you let @=pi/5 ?
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    I remember doing this but I can't remember why...

    Right, judging by what's in the textbook and in my notes, the roots in b are the values for [email protected] for which [email protected] = 0

    And then I guess you do [email protected] = sin^-1(0)
    Divide those by five to get @. That's where you get 2pi/five.
    And then you put that angle in
    Sin2pi/5= the roots to b

    I'm not sure that's right but that's how I would tackle it.
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    Ok I set @ = pi/5 and got 0 = 16sin^4(pi/5) -20sin^2(pi/5) + 5 used my answer to (b) to find sin(pi/5). I typed into my calc sin(pi/5) to find the approx value and then determined which root from (b) corresponded to the calc value for sin(pi/5). so got sqrt(5/8 - sqrt(5)/8). Did the same for sin(2pi/5). Now I don't know whether my solution was justified enough as it says "explain clearly" so is there a proper method for determining which out of the 4 roots was correct, rather than just using the calc?
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    (Original post by thers)
    Ok I set @ = pi/5 and got 0 = 16sin^4(pi/5) -20sin^2(pi/5) + 5 used my answer to (b) to find sin(pi/5). I typed into my calc sin(pi/5) to find the approx value and then determined which root from (b) corresponded to the calc value for sin(pi/5). so got sqrt(5/8 - sqrt(5)/8). Did the same for sin(2pi/5). Now I don't know whether my solution was justified enough as it says "explain clearly" so is there a proper method for determining which out of the 4 roots was correct, rather than just using the calc?
    Sketch y = sin x and indicate the approximate value of sin (pi/5) and sin (2pi/5) ?
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    (Original post by Mr M)
    Sketch y = sin x and indicate the approximate value of sin (pi/5) and sin (2pi/5) ?
    Ok that should suffice. Thanks for the help
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    (Original post by thers)
    Ok I set @ = pi/5 and got 0 = 16sin^4(pi/5) -20sin^2(pi/5) + 5 used my answer to (b) to find sin(pi/5). I typed into my calc sin(pi/5) to find the approx value and then determined which root from (b) corresponded to the calc value for sin(pi/5). so got sqrt(5/8 - sqrt(5)/8). Did the same for sin(2pi/5). Now I don't know whether my solution was justified enough as it says "explain clearly" so is there a proper method for determining which out of the 4 roots was correct, rather than just using the calc?
    I'm not sure if a calc answer would suffice. I'm doing that chapter soon so if I figure out another way asides from what I've said before I'll let you know. (:


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    (Original post by PapercutMagnet)
    I'm not sure if a calc answer would suffice. I'm doing that chapter soon so if I figure out another way asides from what I've said before I'll let you know. (:
    It's almost like I'm invisible.
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    (Original post by Mr M)
    It's almost like I'm invisible.
    I'm sorry.
    I'm not entirely sure what you meant by your first post.
    Diagrams are always a good option. Whether it'd be valid enough just based on an approximation I'm not sure though. :/


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    (Original post by PapercutMagnet)
    Whether it'd be valid enough just based on an approximation I'm not sure though. :/
    I am and it is.
 
 
 
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