Elements of Trigonometry, and Trigonometrical Analysis, Preliminary to the Differential Calculus: Fit for Those Who Have Studied the Principles of Arithemetic and Algebra, and Six Books of Euclid
Elements of Trigonometry, and Trigonometrical Analysis, Preliminary to the Differential Calculus: Fit for Those Who Have Studied the Principles of Arithemetic and Algebra, and Six Books of Euclid
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1837 Excerpt: ... lies between--and +, or when 9 lies between 0 and 2. Such a transition would require a continual correction, amounting, in fact, to the process of the last article: but tan-1tanj; is, by definition, the angle which lies between--it and + g, and has x for its tangent. The student should now prove the following theorems ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1837 Excerpt: ... lies between--and +, or when 9 lies between 0 and 2. Such a transition would require a continual correction, amounting, in fact, to the process of the last article: but tan-1tanj; is, by definition, the angle which lies between--it and + g, and has x for its tangent. The student should now prove the following theorems, illustrative of the limitation of F _1, as distinguished from F_i. T = 3-14159265352 which is correct, with the exception of the last place. all similar equations, and explain under what limitations they are true. It must be observed that every such equation becomes true (134.) when sin_i, &c. are substituted for sin-1, &c. But it does not follow that the same value of m in the general equation sin_ia: = 2ffl + sin lx = (2m + l)5r--sin-1a; must be applied on both sides of the equation. (150.) The angle sin-1 is made, by convention, a periodic angle. It changes through 0, -, 0, --, 0, &c. while x changes through 0, 1, 0, --1,0, &c. If x be greater than 1, the angle sin_, i becomes impossible. If in the expressions for sini and cosx, we write xs/--1 for x, we have 2 Vi---i_!----coshes/--l)The right hand sides of the equations are no longer periodic; and in - the same way as all functions of sines, cosines, &c. may be expressed by exponential functions of x and./--1, so all exponential functions may be expressed by forms of sines and cosines of--1. (151.) We may thus always give to periodic series their correct periodic values, either in terms of the primary functions, sines, &c. which are periodic, or by the introduction of periodic angles, sin-Isin 9, cos-1 cos 9, &c. Having illustrated this point, on which freedom from error mainly depends, I shall proceed in the next chapter to some applications of trigonometry
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Add this copy of Elements of Trigonometry, and Trigonometrical Analysis, to cart. $53.22, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Santa Clarita, CA, UNITED STATES, published 2012 by Hardpress Publishing.
Add this copy of Elements of Trigonometry, and Trigonometrical Analysis, to cart. $79.16, new condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Santa Clarita, CA, UNITED STATES, published 2012 by Hardpress Publishing.
