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Math Help - Trigonometric Identity

  1. #1
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    Trigonometric Identity

    So I have a question that is:

    Given that cos theta = 24/25 and theta is in Quadrant I, determine sin 2theta, cos 2theta and tan 2theta. Which quadrant is 2theta in?

    I already solved the sin, cos and tan portion of the problem

    sin 2theta = 336/625
    cos 2theta = 527/625
    tan 2theta = 336/527

    but the issue I have is I have no idea how to determine which quadrant 2theta is in.

    Any help would be appreciated! Thanks in advance!
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  2. #2
    Junior Member beebe's Avatar
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    Re: Trigonometric Identity

    You've already shown:
    sin(2\theta)>0
    cos(2\theta)>0
    tan(2\theta)>0

    What does each of these inequalities tell you about 2\theta?
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  3. #3
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    Re: Trigonometric Identity

    Too be honest I am not really sure >.<

    that 2 theta is positive?
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  4. #4
    Junior Member beebe's Avatar
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    Re: Trigonometric Identity

    It might help if you consider 2\theta as a single variable. That is, let 2\theta=a (a is for angle!) Now, each of the values you calculated is positive.

    What quadrants can a be in to make sin(a) positive?
    What quadrants can a be in to make cos(a) positive?
    What quadrants can a be in to make tan(a) positive?
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  5. #5
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    Re: Trigonometric Identity

    oh I get it .. so Quadrant I. Because sin, cos and tan are all positive in Quadrant I
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