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Math Help - tan (A + B)

  1. #1
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    tan (A + B)

    If A = arctan(2/3) and B = arctan(1/2), find tan (A + B).
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  2. #2
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    Quote Originally Posted by magentarita View Post
    If A = arctan(2/3) and B = arctan(1/2), find tan (A + B).
    Hint:

    \tan{(\alpha + \beta)} = \frac{\tan{\alpha} + \tan{\beta}}{1 - \tan{\alpha}\tan{\beta}}.
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  3. #3
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    I know but...

    Quote Originally Posted by Prove It View Post
    Hint:

    \tan{(\alpha + \beta)} = \frac{\tan{\alpha} + \tan{\beta}}{1 - \tan{\alpha}\tan{\beta}}.
    I know this is the correct formula to use. My problem concerns the arctan values given. I also know that arctan means tangent inverse but how do I use the given arctan values in this formula?
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  4. #4
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    \tan{(\arctan{\theta})} = \theta.
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  5. #5
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    are you

    Quote Originally Posted by Prove It View Post
    \tan{(\arctan{\theta})} = \theta.
    Are you saying that arctan(2/3) = 2/3 and that
    arctan(1/2) = 1/2?

    If that's the case, then A = 2/3 and B = 1/2. Is this what needs to plugged into the formula for tan (A + B)?
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  6. #6
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by magentarita View Post
    Are you saying that arctan(2/3) = 2/3 and that
    arctan(1/2) = 1/2?

    If that's the case, then A = 2/3 and B = 1/2. Is this what needs to plugged into the formula for tan (A + B)?
    No. What he's saying is that \tan\!\left(\arctan\!\left(\tfrac{2}{3}\right)\rig  ht)=\tfrac{2}{3} and \tan\!\left(\arctan\!\left(\tfrac{1}{2}\right)\rig  ht)=\tfrac{1}{2}.

    Your A and B values are still those arctangent values, but when you substitute them into your identity, you take into consideration what ProveIt told you (and what I elaborated above).
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  7. #7
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    can you

    Quote Originally Posted by Chris L T521 View Post
    No. What he's saying is that \tan\!\left(\arctan\!\left(\tfrac{2}{3}\right)\rig  ht)=\tfrac{2}{3} and \tan\!\left(\arctan\!\left(\tfrac{1}{2}\right)\rig  ht)=\tfrac{1}{2}.

    Your A and B values are still those arctangent values, but when you substitute them into your identity, you take into consideration what ProveIt told you (and what I elaborated above).
    Can you show me how this is done?
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  8. #8
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    Quote Originally Posted by magentarita View Post
    Can you show me how this is done?
    A = \arctan \left( \frac{2}{3} \right) \Rightarrow \tan A = \frac{2}{3}.

    B = \arctan \left( \frac{1}{2} \right) \Rightarrow \tan B = \frac{1}{2}.
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  9. #9
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    ok

    Quote Originally Posted by mr fantastic View Post
    A = \arctan \left( \frac{2}{3} \right) \Rightarrow \tan A = \frac{2}{3}.

    B = \arctan \left( \frac{1}{2} \right) \Rightarrow \tan B = \frac{1}{2}.
    This is exactly what I thought.
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