| 单词 | secant |
| 例句 | We use the notation to represent the slope of the secant line connecting two points. Precalculus 2021-12-01T00:00:00Z If we choose to change y instead of x by the same incremental value h, then the secant line is parallel to the y-axis and so is the tangent line. Calculus, Volume 3 2016-03-30T00:00:00Z Choose any other point A on the circle, and draw the secant line OA. Calculus, Vol 2 2016-03-30T00:00:00Z The sine, cosine, secant, and cosecant functions have a period of 2π. Calculus, Volume 1 2016-03-30T00:00:00Z The secant of an angle is the same as the secant of its opposite. Algebra and Trigonometry 2015-02-13T00:00:00Z We can calculate the slope of the line connecting the two points and called a secant line, by applying the slope formula, Precalculus 2021-12-01T00:00:00Z We can calculate the slope of the secant line by dividing the difference in z-values by the length of the line segment connecting the two points in the domain. Calculus, Volume 3 2016-03-30T00:00:00Z An angle formed by two secants, a secant and a tangent, or two tangents, drawn to a circle from an external point, is measured by half the difference of the intercepted arcs. The Teaching of Geometry 2011-10-12T02:00:52.133Z Such a line is called a secant line. Calculus, Volume 1 2016-03-30T00:00:00Z The secant, cotangent, and cosecant are all reciprocals of other functions. Algebra and Trigonometry 2015-02-13T00:00:00Z So if the secant of angle t is 2, the secant of is also 2. Precalculus 2021-12-01T00:00:00Z Then the lines through A in α are divided into two classes by reference to l, namely, the secant lines which intersect l, and the non-secant lines which do not intersect l. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z If from a point without a circle a secant is drawn, the product of the secant and its external segment is constant in whatever direction the secant is drawn. The Teaching of Geometry 2011-10-12T02:00:52.133Z We formally define a secant line as follows: Calculus, Volume 1 2016-03-30T00:00:00Z The secant is the reciprocal of the cosine function, the cotangent is the reciprocal of the tangent function, and the cosecant is the reciprocal of the sine function. Algebra and Trigonometry 2015-02-13T00:00:00Z Then, we can find the other trigonometric functions easily because we know that the reciprocal of sine is cosecant, the reciprocal of cosine is secant, and the reciprocal of tangent is cotangent. Precalculus 2021-12-01T00:00:00Z If, however, the rays a1 and a2 are secants meeting at A, then the ruled quadric surface becomes a cone of the second order, having A as centre. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z His father stood over him in wonder while he filled a sheet of paper with sines, cosines, secants, and such things. Harper's Round Table, June 4, 1895 The accuracy of approximating the rate of change of the function with a secant line depends on how close x is to a. Calculus, Volume 1 2016-03-30T00:00:00Z Cosine and secant are even; sine, tangent, cosecant, and cotangent are odd. Algebra and Trigonometry 2015-02-13T00:00:00Z DEF, is termed a “secant”; if it touches the circle, e.g. Encyclopaedia Britannica, 11th Edition, Volume 6, Slice 4 "Cincinnatus" to "Cleruchy" This gives the theorem:— On a twisted cubic any two points may be taken as centres of projective pencils which generate the cubic, corresponding planes being those which meet on the same secant. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z And thus much of the secants, the Tangents doe follow. The Way To Geometry Figure 2.6 Solving the Tangent Problem: As x approaches a, the secant lines approach the tangent line. Calculus, Volume 1 2016-03-30T00:00:00Z Note that, because cosine is an even function, secant is also an even function. Algebra and Trigonometry 2015-02-13T00:00:00Z The complement of the logarithm of a sine, tangent, or secant. The Sailor's Word-Book An Alphabetical Digest of Nautical Terms, including Some More Especially Military and Scientific, but Useful to Seamen; as well as Archaisms of Early Voyagers, etc. The lines where a plane cuts its corresponding plane are secants. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z And 29 If the angle of the secant and touch line be equall to an assigned rectilineall angle, the angle in the opposite section shall likewise be equall to the same. The Way To Geometry Note that finding the average velocity of a position function over a time interval is essentially the same as finding the slope of a secant line to a function. Calculus, Volume 1 2016-03-30T00:00:00Z That is, The graph of cosecant, which is shown in Figure 7, is similar to the graph of secant. Algebra and Trigonometry 2015-02-13T00:00:00Z That which is made by a right line, whether tangent or secant, with the circumference of a circle. The Sailor's Word-Book An Alphabetical Digest of Nautical Terms, including Some More Especially Military and Scientific, but Useful to Seamen; as well as Archaisms of Early Voyagers, etc. A secant improper may be considered, to use the language of coordinate geometry, as a secant with imaginary points of intersection. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z I want secant fifteen less one times thirty-two hundred. Skylark Three Furthermore, to find the slope of a tangent line at a point a, we let the x-values approach a in the slope of the secant line. Calculus, Volume 1 2016-03-30T00:00:00Z The procedure for secant is very similar, because the cofunction identity means that the secant graph is the same as the cosecant graph shifted half a period to the left. Algebra and Trigonometry 2015-02-13T00:00:00Z Seated at the same table as herself was a skilful sailor, using logarithms, secants and cosecants, polar distances and hour angles, as if he were in some university class-room. The Captain of the Kansas Hence:— Through every point in space not on the twisted cubic one and only one secant to the cubic can be drawn. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z He felt the necessity of gaining a more firm footing, and turned toward the road by the shortest secant line. The Vicomte de Bragelonne Or Ten Years Later being the completion of "The Three Musketeers" And "Twenty Years After" We can also calculate the slope of a secant line to a function at a value a by using this equation and replacing x with a + h, where h is a value close to 0. Calculus, Volume 1 2016-03-30T00:00:00Z The secant function is the reciprocal of the cosine function. Algebra and Trigonometry 2015-02-13T00:00:00Z The distances at which it is heard vary as the secants of a circle, the radius in this case being a length which is the closest approach of the ear to the bell. Cyclopedia of Telephony & Telegraphy Vol. 1 A General Reference Work on Telephony, etc. etc. We shall see this congruence consists of all lines which cut a twisted cubic twice, or of all secants to a twisted cubic. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z See clear. line, n. stripe, streak; cord, rope, thread, string, cable; course, route; branch, department; boundary, contour, periphery, circumference, outline; lineament; row, series, rank, file; secant; hachure, hatching. Putnam's Word Book These two expressions for calculating the slope of a secant line are illustrated in Figure 3.3. Calculus, Volume 1 2016-03-30T00:00:00Z Finally, in quadrant IV, “Class,” only cosine and its reciprocal function, secant, are positive. Algebra and Trigonometry 2015-02-13T00:00:00Z The whole secret of avoiding shipwreck is to try and pass from the secant to the tangent. The Man Who Laughs This inclination was small, and its secant varies slowly, so that any slight error in this angle would not appreciably affect the result. Experimental Determination of the Velocity of Light Made at the U.S. Naval Academy, Annapolis Accordingly, an observation of the temperature produced by solar radiation at a zenith distance whose secant is twice that of the secant of 17° 12', viz., Scientific American Supplement, No. 458, October 11, 1884 We will see that each of these two methods for finding the slope of a secant line is of value. Calculus, Volume 1 2016-03-30T00:00:00Z So if the secant of angle is 2, the secant of is also 2. Algebra and Trigonometry 2015-02-13T00:00:00Z The bullet had entered near the point of the shoulder, but a little below, so that it had merely cut a secant through the curve of the muscle. The Claim Jumpers He felt the necessity of gaining a firmer footing, and turned towards the road by the shortest secant line. The Man in the Iron Mask At other inclinations, the interval will be the difference of the secants from the secant of the inclination, or angle of refraction of the principal beam. A History of Science — Volume 3 Figure 3.3 We can calculate the slope of a secant line in either of two ways. Calculus, Volume 1 2016-03-30T00:00:00Z For the four trigonometric functions, sine, cosine, cosecant and secant, a revolution of one circle, or will result in the same outputs for these functions. Algebra and Trigonometry 2015-02-13T00:00:00Z Figure 4.25 The Mean Value Theorem says that for a function that meets its conditions, at some point the tangent line has the same slope as the secant line between the ends. Calculus, Volume 1 2016-03-30T00:00:00Z For the following exercises, use both Newton’s method and the secant method to calculate a root for the following equations. Calculus, Volume 1 2016-03-30T00:00:00Z For the following exercises, use the secant method, an alternative iterative method to Newton’s method. Calculus, Volume 1 2016-03-30T00:00:00Z Furthermore, the secant lines themselves approach the tangent line to the function at a, which represents the limit of the secant lines. Calculus, Volume 1 2016-03-30T00:00:00Z Because the cosine is never more than 1 in absolute value, the secant, being the reciprocal, will never be less than 1 in absolute value. Algebra and Trigonometry 2015-02-13T00:00:00Z When the cosine function is zero, the secant is undefined. Algebra and Trigonometry 2015-02-13T00:00:00Z Vertical and phase shifts may be applied to the cosecant function in the same way as for the secant and other functions.The equations become the following. Algebra and Trigonometry 2015-02-13T00:00:00Z Use the reciprocal relationship of the cosine and secant functions to draw the cosecant function. Algebra and Trigonometry 2015-02-13T00:00:00Z Just as we have used two different expressions to define the slope of a secant line, we use two different forms to define the slope of the tangent line. Calculus, Volume 1 2016-03-30T00:00:00Z Where the graph of the cosine function decreases, the graph of the secant function increases. Algebra and Trigonometry 2015-02-13T00:00:00Z Q&A Do the vertical shift and stretch/compression affect the secant’s range? Algebra and Trigonometry 2015-02-13T00:00:00Z The secant and cosecant are both periodic functions with a period of gives a shifted, compressed, and/or stretched secant function graph. Algebra and Trigonometry 2015-02-13T00:00:00Z Write the equation for the graph in Figure 1 in terms of the secant function and give the period and phase shift. Algebra and Trigonometry 2015-02-13T00:00:00Z To understand this notation better, recall that the derivative of a function at a point is the limit of the slopes of secant lines as the secant lines approach the tangent line. Calculus, Volume 1 2016-03-30T00:00:00Z Where the graph of the cosine function increases, the graph of the secant function decreases. Algebra and Trigonometry 2015-02-13T00:00:00Z To sum up, only two of the trigonometric functions, cosine and secant, are even. Algebra and Trigonometry 2015-02-13T00:00:00Z |
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