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. 1841 Excerpt: ...+ S).. + (-1) ---, / sin 0. In employing these formulae for the purposes of calculating sin" 0, we have only to follow the law indicated by the first terms, and to stop at the term which involves the first negative angle; and we must take only half of the coefficient of the last term when it involves the angle zero. ...
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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. 1841 Excerpt: ...+ S).. + (-1) ---, / sin 0. In employing these formulae for the purposes of calculating sin" 0, we have only to follow the law indicated by the first terms, and to stop at the term which involves the first negative angle; and we must take only half of the coefficient of the last term when it involves the angle zero. 1nverse Trigonometrical functions of an angle. 141. Since the sine, cosine, &c. of an angle do not increase indefinitely with the angle, but vary within certain limits only, so that whatever values they have when the angle equals a, they receive the same when the angle equals a + 2ir, a + 4-, &c, they are called periodic quantities to distinguish them from continually increasing quantities. We have hitherto chiefly confined our reasonings to the case where only the sines, cosines, &c. of known angles enter into the calculation; but it is frequently necessary to consider the case where the angles themselves, as determined by their sines, cosines, &c. are introduced; and there is, as has been stated, an essential difference between these cases; for in the former the quantities have each only a single value, whereas in the latter they have an infinite number of values. Thus sin SO' has only one value, viz. 1; but angle whose sine = 1, has an infinite number of values comprised in the general expression (Art. 31) The notation usually employed to express an angle whose sine is x, an angle whose cosine is x, 8tc. is sin_1J?, cos-1a?, &c.; they are called inverse Trigonometrical functions of the angle, in the same way as the Trigonometrical Ratios themselves are called direct Trigonometrical functions of the angle. 142. The reason for the above notation is the following. If an operation denoted by f be performed upon...
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Add this copy of A Treatise on Trigonometry, and on Trigonometrical to cart. $65.41, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 2016 by Palala Press.
