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    A) +- 0.55

    C) 0.55

    Why is the answer A, I am sure the solution is simple, and can you please not use CAST as an explanation.

    Thank you.
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    (Original post by fnatic NateDestiel)
    A) +- 0.55

    C) 0.55

    Why is the answer A, I am sure the solution is simple, and can you please not use CAST as an explanation.

    Thank you.
    How am I to explain it if I do not use the range in which tan is positive?

    So - tan is positive between 0 and 90 - in this range sin is also positive

    Also - tan is positive between 180 and 270 - in this range sin is negative


    Given this - sin could be either positive or negative
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    Posted from TSR Mobile

    Use the identity cot^2 + 1 = cosec^2

    to find sin you will up having to take a square root that leads to +-
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    (Original post by fnatic NateDestiel)
    A) +- 0.55

    C) 0.55

    Why is the answer A, I am sure the solution is simple, and can you please not use CAST as an explanation.

    Thank you.
    Draw a right angled triangle, note that tan theta= opposite/adjacent. Use pythag to find the hypotenuse
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    (Original post by TenOfThem)
    How am I to explain it if I do not use the range in which tan is positive?

    So - tan is positive between 0 and 90 - in this range sin is also positive

    Also - tan is positive between 180 and 270 - in this range sin is negative


    Given this - sin could be either positive or negative
    I understand your first point and it is easily solvable on the calculator.

    And I understand your second point, but I don't get how it is related to the question.

    Because I only get -0.55 when tan theta is - 2/3.
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    That'll be useful in later life...
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    (Original post by BankOfPigs)
    Posted from TSR Mobile

    Use the identity cot^2 + 1 = cosec^2

    to find sin you will up having to take a square root that leads to +-
    I have tried this method, but only get the identities proving other identities or cancelling eachother out

    (Original post by Gome44)
    Draw a right angled triangle, note that tan theta= opposite/adjacent. Use pythag to find the hypotenuse
    I did this initially, but I only get the positive answer..
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    (Original post by fnatic NateDestiel)
    I have tried this method, but only get the identities proving other identities or cancelling eachother out


    I'm not really too sure what you mean.

    Cot^2 x + 1 = cosec^2 x

    since tan = 2/3 cot = 3/2

    so (3/2)^2+1 = 1/sin^2
    13/4 = 1/ sin^2
    4/13 = sin^2 x

    Now this leads to 2 roots. If you aren't sure what I mean, do the substituion y = sin x

    so 4/13 = y^2
    This has 2 roots, one negative, one positive.
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    (Original post by BankOfPigs)
    I'm not really too sure what you mean.

    Cot^2 x + 1 = cosec^2 x

    since tan = 2/3 cot = 3/2

    so (3/2)^2+1 = 1/sin^2
    13/4 = 1/ sin^2
    4/13 = sin^2 x

    Now this leads to 2 roots. If you aren't sure what I mean, do the substituion y = sin x

    so 4/13 = y^2
    This has 2 roots, one negative, one positive.
    Oh I see thank you, this makes sense, one other guy on CC posted this; "You need to consider all the angles for which tan theta = 2/3. The first one is 33.69 degrees, but there are infinitely many, so find the next one and consider that." which also works.

    Thanks though!
 
 
 
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