Pre-Calculus

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For what values of x is it true that |sin(x)-x| < 0.01?

  • Pre-Calculus -

    I have spend 20 min on this,with no results. I went the Taylor expansion of sin(x), and it didn't help. When you get a solution, please post it. FYI, I graphed it, and was surprised. It reminded me how accurate the small angle approximation is.

  • Pre-Calculus -

    I looked at the solution to
    |sinx -x| = .01 and using Newton's Method found
    x = ±.392493378

    then testing, I found the above to be true for

    -.3925 < x < + .3924

    x is in radians

    (for sinx - x = .01 my iteration expression was
    (xcosx - sinx + .01)/(cosx - 1) )

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