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Simple harmonic motion (SHM( is defined by the second order differential equation:
d2y/dt2 = -ky
where y is a fubction of time, t and is the displacement (relative to the central position), and k is a positive constant.
The equation says is that at any given position of the object undergoing SHM, its acceleration is proportional to its displacement from, and directed towards the central position.
The sine and cosine functions are solutions to the differential equation.
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Why are sine and cosine functions called harmonic?
Sinusoid shape of the sine and cosine functions appear as oscillations. If an object is moving in a straight line and its position (function of time) can be described as sinusoid then it is referred to as a simple harmonic motion.
What are the trigonometric functions?
sine, cosine, tangent, cosecant, secant and cotangent.
What are circular functions?
Sine, Cosine, Tangent, Cotangent, secant and cosecant
What is trigonometry's circular function?
The basic circular functions are sine, cosine and tangent. Then there are their reciprocals and inverses.
What are the six trigonometric functions of special angles?
sine, cosine, tangent, cosecant, secant and cotangent.
