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Math Help - Help angle of inclination

  1. #1
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    Help angle of inclination

    how do you calculate the angle of inclination of y=x2 to the nearest degree?

    please help!!!
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    Re: Help angle of inclination

    A function does not have an "angle of inclination"! I assume you mean "the angle of inclination with the x-axis of the tangent to the curve y= x^2 at any point".

    If \theta is the angle the tangent line to y= f(x) makes with x-axis than tan(\theta)= df/dx.
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    Re: Help angle of inclination

    so what am i suppose to do with that? the answer is 63 degrees but how do i get that?
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    Re: Help angle of inclination

    Quote Originally Posted by HallsofIvy View Post
    A function does not have an "angle of inclination"! I assume you mean "the angle of inclination with the x-axis of the tangent to the curve y= x^2 at any point".

    If \theta is the angle the tangent line to y= f(x) makes with x-axis than tan(\theta)= df/dx.

    so what am i suppose to do with that? the answer is 63 degrees but how do i get that?
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  5. #5
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    Re: Help angle of inclination

    Quote Originally Posted by pnfuller View Post
    how do you calculate the angle of inclination of y=x2 to the nearest degree?
    please post the entire problem as stated from its source ... I've never heard of the angle of inclination of a function, either.
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    Re: Help angle of inclination

    let l be the tangent line to the parabola y=x^2 at the point (1,1). the angle of inclination of l is the angle θ that l makes with the positive direction of the x-axis. calculate θ correct to the nearest degree. i know the answer should be 63 degrees but how?
    Quote Originally Posted by skeeter View Post
    please post the entire problem as stated from its source ... I've never heard of the angle of inclination of a function, either.
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  7. #7
    MHF Contributor MarkFL's Avatar
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    Re: Help angle of inclination

    The slope of the tangent line is found by evaluating the derivative of the function at the given x-coordinate.

    y'(1)=2(1)=2

    The slope m of a line is related to its angle of inclination \theta by m=\tan(\theta).

    Hence, the angle of inclination is \theta=\tan^{-1}(2)\approx63^{\circ}.
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