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Math Help - Expressions involving trigonometry

  1. #1
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    Expressions involving trigonometry

    I did a past paper which had the following question:

    Let p = sin40 and q = cos110. Give your answers to the following in terms of p and/or q.

    Write down an expression for
    (i) sin140

    (ii) cos70.

    Apparently the answer for (i) is p = sin140 and for (ii) cos70 = -q

    I do not understand why is that the answer. Is it anything to do with the CAST unit circle idea? If it is then it would not make sense for cos.

    Please explain!

    Thanks
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  2. #2
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    (i) Use the fact that you know that sin(v)=sin(180-v)
    (ii) Use the fact that you know that -cos(v)=cos(180-v)

    When you're facing problems involving angles that you "haven't seen" earlier in the problem, the solution often has something to do with the trig. identities! keep it in mind and learn how to derive them from the unit circle (the basic onces)!
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  3. #3
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    Quote Originally Posted by CSG18 View Post
    Is it anything to do with the CAST unit circle idea? If it is then it would not make sense for cos.
    Yes it does, good work.

    \cos (180- \theta) = -\cos\theta

    Think about this q = \cos 110  = \cos (180 - 70)  = -\cos 70
    Last edited by pickslides; March 13th 2010 at 12:46 PM. Reason: bad latex
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  4. #4
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    Smile

    Thanks for your help!

    I understand it now, but just to confirm, the reason why there is a minus sign in: -Cos(x) = cos(180-x) is because in the unit circle cos is only positive between 0 to 90 degrees and 270 to 360 degrees (I am aware it goes on).

    What would be the equation for tan(x)?

    Would it be -tan(x) = tan(180-x) ???
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  5. #5
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    Quote Originally Posted by CSG18 View Post

    Would it be -tan(x) = tan(180-x) ???
    Sounds good to me.
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