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Math Help - Circular Functions Problem

  1. #1
    Junior Member
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    Circular Functions Problem

    How do I go about answering these two questions with relation to the attached image?
    Find the values of the following:

    a) tan(\pi-\theta)
    b) tan(-\theta)

    Thanks.
    Attached Thumbnails Attached Thumbnails Circular Functions Problem-circle.png  
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  2. #2
    MHF Contributor
    Grandad's Avatar
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    Hello user_5
    Quote Originally Posted by user_5 View Post
    How do I go about answering these two questions with relation to the attached image?
    Find the values of the following:

    a) tan(\pi-\theta)
    b) tan(-\theta)

    Thanks.
    Two things you need to know first:

    • \tan\theta = \frac{\sin\theta}{\cos\theta}


    • the co-ordinates of any point, P, on the unit circle are (\cos\theta, \sin\theta) where \theta is the angle through which OP has rotated anticlockwise from the positive x-axis.

    So, in the diagram, \cos\theta = \frac12 and \sin\theta=\frac{\sqrt3}{2} and so

    \tan\theta=\frac{\sqrt3}{2}\div\frac{1}{2}=\sqrt3

    OK, so how do we find \tan(\pi-\theta)?

    • Look at the point on the unit circle where the angle is (\pi-\theta).


    • Work out its coordinates (a,b) by reflecting the first point in the y-axis.


    • Now write down \cos(\pi-\theta) and \sin(\pi - \theta)


    • Divide as I did above to give \tan(\pi-\theta)


    Do \tan(-\theta) in exactly the same way.

    Can you complete it now?

    Grandad
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  3. #3
    Junior Member
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    Apr 2009
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    Ahh, thanks I get it now. (:
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