Secant (trigonometry) Secant (trigonometry), one of the fundamental ratios of trigonometry.
Publié le 12/05/2013
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Secant (trigonometry) Secant (trigonometry), one of the fundamental ratios of trigonometry. A ratio is a proportional relationship between two numbers calculated by dividing one number by the other. Secant embodies the relationship between the lengths of the sides of a right triangle (a triangle with a 90° angle) and the magnitudes of the angles. This relationship means that varying one value, such as the length of a side, requires another value, such as the magnitude of an angle, to change in a predictable way. The secant, usually abbreviated sec, of one of the acute (less than 90°) angles of a right triangle is equal to the length of the longest side, called the hypotenuse, divided by the length of the side adjacent to the acute angle: . Secant smoothly increases in numerical value, starting from 1 at 0° and approaching infinity as the angle increases to 90°. Secant 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 secant of ? is equal to the length of the line connecting the point to the circle's center divided by the horizontal distance of the point from the y axis. Secant smoothly increases in numerical value from negative infinity to -1 as ? increases from 90° to 180° and then decreases again, approaching negative infinity as ? goes from 180° to 270°. The function is discontinuous at 270°, flipping from negative infinity to positive infinity and then decreasing to 1 as ? moves from 270° to 360°. Cosine is secant's reciprocal function. The cosine, usually abbreviated cos, 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: . Sine, Cosecant, Tangent, Cotangent. Microsoft ® Encarta ® 2009. © 1993-2008 Microsoft Corporation. All rights reserved.
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