Small Angle Approximation

Some articles on angle, small, approximation:

Pendulum (mathematics) - Small-angle Approximation
... If it is assumed that the angle is much less than 1 radian, or , then substituting for sin θ into Eq. 1 using the small-angle approximation, , yields the equation for a harmonic oscillator, The error due to the approximation is of order θ 3 (from the Maclaurin series for sin θ) ... semi-amplitude of the oscillation (that is, the maximum angle between the rod of the pendulum and the vertical) ...
Small-angle Approximation
... The small-angle approximation is a useful simplification of the basic trigonometric functions which is approximately true in the limit where the angle approaches zero ... the Taylor series for the basic trigonometric functions to a second-order approximation ... This truncation gives , where θ is the angle in radians ...

Famous quotes containing the words small and/or angle:

    Nothing would give up life;
    Even the dirt kept breathing a small breath.
    Theodore Roethke (1908–1963)

    The inhabitants of earth behold commonly but the dark and shadowy under side of heaven’s pavement; it is only when seen at a favorable angle in the horizon, morning or evening, that some faint streaks of the rich lining of the clouds are revealed.
    Henry David Thoreau (1817–1862)