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Math Help - solving an equation with terms of trig. and algebraic functions

  1. #1
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    solving an equation with terms of trig. and algebraic functions

    Is there a general approach for solving functions that contain both trig. and algebraic terms? And to be more specific, how does it apply for a problem like this:

    f(x)=x^3+2x+tanx

    In problems with trig. functions, I'm able to determine that for sin(x)=cos(x), x is equal to \frac{\pi}{4}, \frac{5\pi}{4} because it corresponds to an isosceles triangle on the unit circle with equal sides of lengths cos(x) and sin(x), but it wasn't a direct proof.

    Any thoughts?
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  2. #2
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    Re: solving an equation with terms of trig. and algebraic functions

    Quote Originally Posted by Lambin View Post
    Is there a general approach for solving functions that contain both trig. and algebraic terms? And to be more specific, how does it apply for a problem like this:
    f(x)=x^3+2x+tanx
    In problems with trig. functions, I'm able to determine that for sin(x)=cos(x), x is equal to \frac{\pi}{4}, \frac{5\pi}{4} because it corresponds to an isosceles triangle on the unit circle with equal sides of lengths cos(x) and sin(x), but it wasn't a direct proof.
    I have several thoughts about all this.

    One is that f(x)=x^3+2x+\tan(x) is a function. It is not a problem.

    So you need to post real problems. That is, actual questions.
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    Re: solving an equation with terms of trig. and algebraic functions

    Okay. This actually stems from a calculus problem, but I figured I would need to solve it to determine critical points. The reason why I felt that a solution or solutions may exist was because I could imagine that for -(x^3+2x)=tan(x), the two functions would intersect when drawn on a graph.

    QUESTION:

    Does f(x)=x^3+2x+tanx have any local maximum or minimum values? Give reasons for your answer.

    EDIT: Actually, I forgot to take the derivative and then solve the equation. But my question still stands. Also, let me know if I should delete this post, and repost on Calculus.
    Last edited by Lambin; April 12th 2013 at 03:40 PM.
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    Re: solving an equation with terms of trig. and algebraic functions

    Quote Originally Posted by Lambin View Post
    Okay. This actually stems from a calculus problem, but I figured I would need to solve it to determine critical points. The reason why I felt that a solution or solutions may exist was because I could imagine that for -(x^3+2x)=tan(x), the two functions would intersect when drawn on a graph. QUESTION:
    Does f(x)=x^3+2x+tanx have any local maximum or minimum values? Give reasons for your answer.
    Well, very good.
    Now you need to solve 3x^2+2+\sec^2(x)=0. That is a hell of a difficult task.
    I would suggest a graphical solution.
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