Cosine.
Publié le 12/05/2013
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Cosine. Cosine, one of the six fundamental ratios of trigonometry: cosine, sine, secant, cosecant, tangent, and cotangent. (A ratio is a proportional relationship between two numbers calculated by dividing one number by the other.) Cosine embodies the relationship between the magnitudes of the angles of a right triangle--a triangle with one 90° angle--and the lengths of its sides. Varying one value, such as the magnitude of an angle, requires the related value, such as the length of a side, to change in a predictable way. The cosine, usually abbreviated cos, of one of the acute (less than 90°) angles of a right triangle is equal to the length of the side adjacent to the acute angle divided by the length of the longest side, called the hypotenuse: . Cosine smoothly decreases in numerical value from 1 to 0 as the angle increases from 0° to 90°. Cosine is also defined for angles greater than 90° using right triangles inscribed in a circle centered at the point (0,0) on the xy axis: A line drawn from the circle's center to any point on the circle makes an angle, ? , with the x axis. The cosine of ? is equal to the horizontal distance of the point from the y axis divided by the length of the line connecting the point to the circle's center. Cosine smoothly decreases in numerical value from 0 to -1 as ? increases from 90° to 180° and then increases again to 1 as ? goes from 180° to 360°. Secant is cosine's reciprocal function. The secant of an acute angle of a right triangle is equal to the length of the triangle's hypotenuse divided by the length of the side adjacent to the chosen acute angle: . Microsoft ® Encarta ® 2009. © 1993-2008 Microsoft Corporation. All rights reserved.