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Math Help - Evaluating a trigs of trigs

  1. #1
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    Evaluating a trigs of trigs

    Evaluating a trigs of trigs-screen-shot-2012-10-23-10.55.03-am.png

    How does one find the value of tan theta that =1/3

    I tried to work it out using a triangle and inverse trig functions

    If arctan(1/3)=theta then theta = tan(1/3)

    that means we should be able to draw a right angle triangle where the side opposte theta is 1 and the side adjacent is 3

    this would make the hypotenuse sqrt(10)

    however when I use arcsin and arccos to find the angles I get both angles near 18 which would imply that the triangle is not a right triangle.

    Am I on the right track at all?

    perhaps my calculator should be in radian mode? is that the what im missing? I'm not sure.
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  2. #2
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    Re: Evaluating a trigs of trigs

    Quote Originally Posted by kingsolomonsgrave View Post
    Click image for larger version. 

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    How does one find the value of tan theta that =1/3
    I tried to work it out using a triangle and inverse trig functions
    If arctan(1/3)=theta then theta = tan(1/3)
    You have that backwards.
    \tan(\theta)=\frac{1}{3} so \sin(\theta)=\frac{1}{\sqrt{10}}~\&~\cos(\theta) =\frac{3}{\sqrt{10}}

    Now you have \cos(2\theta)=\cos^2(\theta)-\sin^2(\theta)
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  3. #3
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    Re: Evaluating a trigs of trigs

    Evaluate
    Hi,
    I attached a word-file with the solution.
    I hope, does help!
    You can verify with the calculator:
    tan^-1(0.3333333) =18.434932
    2*tan^-1(0.3333333) =36.869863
    cos(36.869863) =0.800000
    (Use-modus is degree, not radian)

    Best regards,
    Stefan
    Attached Files Attached Files
    Last edited by StefanTM; October 24th 2012 at 11:31 PM.
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