### Some articles on *angle, small, approximation*:

Pendulum (mathematics) - Small-angle Approximation

... If it is assumed that the

... 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

... 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)

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