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The sine and the cosine functions, for example, are used to describe simple harmonic motion, which models many natural phenomena, such as the movement of a mass attached to a spring and, for small angles, the pendular motion of a mass hanging by a string. The sine and cosine functions are one-dimensional projections of uniform circular motion.
The figure shows how the sign of the sine function varies as the angle changes quadrant. Because the x - and y -axes are perpendicular, this Pythagorean identity is equivalent to the Pythagorean theorem for triangles with hypotenuse of length 1 (which is in turn equivalent to the full Pythagorean theorem by applying a similar-triangles argument).
In mathematics, sine and cosine are trigonometric functions of an angle.The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle (the hypotenuse), and the cosine is the ratio of the length of the adjacent leg to that ...
These identities are useful whenever expressions involving trigonometric functions need to be simplified. An important application is the integration of non-trigonometric functions: a common technique involves first using the substitution rule with a trigonometric function, and then simplifying the resulting integral with a trigonometric identity.
Write the functions without "co" on the three left outer vertices (from top to bottom: sine, tangent, secant) Write the co-functions on the corresponding three right outer vertices (cosine, cotangent, cosecant) Starting at any vertex of the resulting hexagon: The starting vertex equals one over the opposite vertex.
The sine and cosine functions are fundamental to the theory of periodic functions, [63] such as those that describe sound and light waves. Fourier discovered that every continuous , periodic function could be described as an infinite sum of trigonometric functions.
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