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Math Help - Half Angle Formulas

  1. #1
    Member purplec16's Avatar
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    Half Angle Formulas

    tan \frac{3\pi}{8}

    Use tan 2\theta to find the exact value

    Im stuck because I dont know which half-angle formula do I use?
    Last edited by purplec16; March 17th 2010 at 06:34 AM.
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  2. #2
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    Quote Originally Posted by purplec16 View Post
    Can someone please help me with this question I need it in like 10-20 mins

    tan \frac{3\pi}{8}

    Use tan 2\theta to find the exact value
    If 3π/8 = θ, then 3π/4 = 2θ
    Now tan(2θ) = 2*tanθ/(1-tan^2θ)........(1)

    tan(2θ) = tan(3π/4) = ..........?
    Substitute this value in the eq.(1) and solve for tanθ
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  3. #3
    Member purplec16's Avatar
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    Quote Originally Posted by sa-ri-ga-ma View Post
    If 3π/8 = θ, then 3π/4 = 2θ
    Now tan(2θ) = 2*tanθ/(1-tan^2θ)........(1)

    tan(2θ) = tan(3π/4) = ..........?
    Substitute this value in the eq.(1) and solve for tanθ
    I need to solve it using one of the half-angle formulas
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  4. #4
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    Quote Originally Posted by purplec16 View Post
    I need to solve it using one of the half-angle formulas
    I have given the half angle formula.
    If 2θ = 3π/4, half of that angle is θ = 3π/8 which is the required angle.
    I have observed that you are not following our instructions. Every time you expect the complete solution. It is not good for any student who wants to study the subject.
    In my post, you have to find the value of tan(3π/4), simplify the expression, solve the quadratic equation to get tanθ, i.e. tan(3π/8).
    Can you try now?
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  5. #5
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    \tan\left(\frac{\theta}{2}\right) = \pm \sqrt{\frac{1-\cos{\theta}}{1+\cos{\theta}}}

    if \frac{\theta}{2} = \frac{3\pi}{8} , then \theta = \frac{3\pi}{4}

    also note that \frac{3\pi}{8} is a quad I angle, so \tan\left(\frac{3\pi}{8}\right) > 0<br />

    plug and chug using the given half-angle formula.
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