Sine
Sine is a trigonometric function derived from the Latin sinus meaning curve. In a right triangle the sine of an angle (sin) is defined as the length of the side of the triangle opposite the angle divided by the length of the hypotenuse. sin = opp/hyp The values of the sine of an angle are always between zero and one for a right triangle. This function can be extended beyond 90º by using Cartesian coordinates. Values of the sine function can then be either positive or negative but still range between -1 and 1; these values repeat every 360º and therefore this function is considered a periodic function.
The sine function is related to the other six basic trigonometric functions in special relationships.
The sine function is related to the cosine function as: cos = sin (90º - ). The sine function is also related to the tangent function and can be written as: tan = sin/cos. Using these relationships in conjunction with the following the sine function can be related to the other three trigonometric functions, cosecant (csc), secant (sec), and cotangent (cot). csc = 1/sin The Pythagorean theorem for right triangles can be translated into a Pythagorean identity for sines and cosines and often appears as: sin2 + cos2 = 1.
The periodic nature of the sine function makes it important in applications involving the study of periodic phenomena such as light and electricity. A general triangle, not necessarily containing a right angle, can also be analyzed using trigonometric functions. In spherical trigonometry, the sine of an angle of a triangle on the surface of a sphere is important in surveying, navigation and astronomy.
This is the complete article, containing 274 words
(approx. 1 page at 300 words per page).
