Cotangent.
Publié le 06/12/2021
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Cotangent.
Cotangent, one of the six fundamental ratios of trigonometry, along with tangent, sine, cosine, secant, and cosecant. (A ratio is a proportional relationship between two
numbers calculated by dividing one number by the other.) Cotangent 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 of the numbers, such as the length of a side, requires the related number, such as the magnitude of an
angle, to change in a predictable way.
The cotangent, usually abbreviated cot, of one of the acute (less than 90°) angles of a right triangle is equal to the length of the shorter of the two sides adjacent to
the angle divided by the length of the side opposite the angle:
. (The longer adjacent side is called the triangle's hypotenuse).
Cotangent smoothly decreases in numerical value from infinity to 0 as the angle increases from 0° to 90°. The function 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 cotangent of ? is equal to the horizontal distance of the point from
the y axis divided by the vertical distance of the point from the x axis. Cotangent smoothly decreases in numerical value from 0 to negative infinity as ? increases from
90° to 180°. At 180°, cotangent is discontinuous, flipping from negative infinity to positive infinity. The function falls from positive infinity to 0 at 270° and continues to
decline, approaching negative infinity at 360°.
Tangent (abbreviated tan) is cotangent's reciprocal function. The tangent of an acute angle of a right triangle is equal to the length of the side opposite the chosen
acute angle divided by the length of the shorter of the two sides adjacent to the angle:
Microsoft ® Encarta ® 2009. © 1993-2008 Microsoft Corporation. All rights reserved.
.
Cotangent.
Cotangent, one of the six fundamental ratios of trigonometry, along with tangent, sine, cosine, secant, and cosecant. (A ratio is a proportional relationship between two
numbers calculated by dividing one number by the other.) Cotangent 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 of the numbers, such as the length of a side, requires the related number, such as the magnitude of an
angle, to change in a predictable way.
The cotangent, usually abbreviated cot, of one of the acute (less than 90°) angles of a right triangle is equal to the length of the shorter of the two sides adjacent to
the angle divided by the length of the side opposite the angle:
. (The longer adjacent side is called the triangle's hypotenuse).
Cotangent smoothly decreases in numerical value from infinity to 0 as the angle increases from 0° to 90°. The function 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 cotangent of ? is equal to the horizontal distance of the point from
the y axis divided by the vertical distance of the point from the x axis. Cotangent smoothly decreases in numerical value from 0 to negative infinity as ? increases from
90° to 180°. At 180°, cotangent is discontinuous, flipping from negative infinity to positive infinity. The function falls from positive infinity to 0 at 270° and continues to
decline, approaching negative infinity at 360°.
Tangent (abbreviated tan) is cotangent's reciprocal function. The tangent of an acute angle of a right triangle is equal to the length of the side opposite the chosen
acute angle divided by the length of the shorter of the two sides adjacent to the angle:
Microsoft ® Encarta ® 2009. © 1993-2008 Microsoft Corporation. All rights reserved.
.
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