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Math Help - Trigonometric Equations

  1. #1
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    Trigonometric Equations

    I have been given the problem 3/tanx=2sinx I can solve this easily graphically however I am lost algebraically, I think there is squaring and trigonometrical identities involved but this whole thing has really ground me to a halt I have no idea were to start. If someone could give me some pointers that would be great.
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  2. #2
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    Re: Trigonometric Equations

    Quote Originally Posted by maca404 View Post
    I have been given the problem 3/tanx=2sinx I can solve this easily graphically however I am lost algebraically, I think there is squaring and trigonometrical identities involved but this whole thing has really ground me to a halt I have no idea were to start. If someone could give me some pointers that would be great.
    \frac{3\cos{x}}{\sin{x}}=\frac{2\sin^2{x}}{\sin{x}  } , note  \sin{x} \ne 0

    3\cos{x}=2(1-\cos^2{x})

    2\cos^2{x}+3\cos{x}-2=0

    (2\cos{x}-1)(\cos{x}+2)=0

    Can you finish?
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  3. #3
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    Re: Trigonometric Equations

    Just do little bit calculations and proceed
    3 = 2 sin x tanx = 2 sinx ( sinx / cos x ) = 2 sin^2 x / cosx
    So we get 3cosx = 2 sin^2 x
    Now convert sin2x in terms of cos^2 x and you have a quadratic in cos x.
    I am sure you can now solve it further.
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  4. #4
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    Re: Trigonometric Equations

    Ok I see what everyone is getting at now, I will put what I have below but I need to work out the equation from 0 to 2pi. I have the first one worked out not sure how to get the second:

    (2cosx-1)(cosx+2)=0

    cosx + 2 = 0

    cosx = -2

    No Solution

    2 cosx -1 =0

    2 cosx = 1

    cosx = 1/2

    x = cos^-1(1/2)

    x = 1.04 rad


    Now I know there is another but I am usure how to find it ?
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  5. #5
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    Re: Trigonometric Equations

    If you are working up to 2\pi then there will be another angle in the circle that gives cosx=\frac{1}{2}. Your calculator will only give you the one from 0 to \pi
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  6. #6
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    Re: Trigonometric Equations

    I can see graphically that I can find the next angle by simply doing 2pi - 1.04 , Is this is the corret way to do it ?
    Last edited by maca404; January 7th 2013 at 12:12 AM.
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  7. #7
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    Re: Trigonometric Equations

    Yes, that sounds good to me.
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  8. #8
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    Re: Trigonometric Equations

    Review your unit circle ...

    \cos{x}=\frac{1}{2} at x=\frac{\pi}{3} and x=\frac{5\pi}{3}

    Last edited by skeeter; January 7th 2013 at 06:00 AM.
    Thanks from topsquark
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