calculus

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Use an appropriate local linear approximation to estimate the value of cotangent 44 degrees.

  • calculus -

    cotan 45 = 1

    d cotan/dx = -csc^2 x
    d cotan = -csc^2 x dx

    here
    csc^2 45 = (2/sqrt2)^2 = 4/2 = 2
    dx = -1 deg * pi radians/180 deg = -.01745
    and
    y(x+dx) = y(x) + dy/dx * dx
    so
    cotan(44)= cotan (45) - 2(-.01745))
    = 1 + .035
    =1.035

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