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" Since, when an angle is acute its supplement is obtuse, it follows from the preceding proposition, that the sine and cosecant of an obtuse angle are positive, while its cosine, tangent, cotangent, and secant, are negative. "
An Elementary Treatise on Plane & Spherical Trigonometry: With Their ... - Page 41
by Benjamin Peirce - 1845 - 449 pages
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An Analytical Treatise on Plane and Spherical Trigonometry, and the Analysis ...

Dionysius Lardner - Plane trigonometry - 1828 - 434 pages
...polar triangle by changing the sides into the supplements of the angles, and vice 'versa. But since the sine and cosecant of the supplement of an angle are the same as those of the angle itself, and the cosine, tangent, cotangent, and secant of the supplement only...
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The Edinburgh Encyclopędia Conducted by David Brewster, with the ..., Volume 18

Encyclopedias and dictionaries - 1832 - 636 pages
...polar triangle by changing the sides into the supplements of the angles, and vice versa. But since the sine and cosecant of the supplement of an angle are the same as those of the angle itself, and the cosine, tangent, cotangent, and secant of the supplement only...
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An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

Benjamin Peirce - Plane trigonometry - 1845 - 498 pages
...N) = sec. N (114) cosec. ( — N) = — cosec. N; (H5) so that the cosine and secant of the negative of an angle are the same with those of the angle itself; and the sine, tangent, cotangent, and cosecant of the negative of the angle are the negative of those of the...
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An Elementary Treatise on Plane and Spherical Trigonometry: With Their ...

Benjamin Peirce - Trigonometry - 1852 - 398 pages
...— N) = — tang. N (100) cotan. (180° — N) = — cotan. N (101) sec. (180° — N) = — sec. N (102) cosec. (180° — N)= cosec. N; (103) that is,...proposition, that the sine and cosecant of an obtuse angle arc positive, while its cosine, tangent, cotangent, and secant are negative. This proposition must...
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An Elementary Treatise on Plane and Spherical Trigonometry: With Their ...

Benjamin Peirce - Trigonometry - 1852 - 382 pages
...zz — cotan. IV (101) sec. (180° — IV) = — sec. IV (102) cosec. (180° — IV) — cosec. IV; (103) that is, the sine and cosecant of the supplement...tangent, cotangent, and secant of the supplement are the negativeof those of the angle. 62. Corollary. Since, when an angle is acute its supplement is obtuse,...
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An Elementary Treatise on Plane and Spherical Trigonometry: With Their ...

Benjamin Peirce - Plane trigonometry - 1861 - 394 pages
...sec. IV (102) 4 ' — cos. N ' cosec. (180° — IV) = -^~,T = cosec. IV; (103) sin. IV that is, iJie sine and cosecant of the supplement of an angle are...tangent, cotangent, and secant of the supplement are the negatives of those of the angle. 62. Corollary. Since every obtuse angle is the supplement of an acute...
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An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

Benjamin Peirce - Trigonometry - 1861 - 396 pages
...N}= 1 — ,-.=—860. N (102) J — cos. N cosec. (180° — N)= -T— ,, = cosec. N; (103). Siii. JT that is, the sine and cosecant of the supplement of...those of the angle itself ; and the cosine, tangent, vAanyent, and secant of the supplement are the negatives of those of the angle. 62. Corollary. Since...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 532 pages
...b, (48) sec (180° — b) = _losb = —sec b, (49) cosec (180° — 6) = \ = cosec b ; (50) 311' 0 that is, the sine and cosecant of the supplement of an angle are the same as those of the angle itself; and the cosine, tangent, cotangent, and secant are the negatives of those...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 518 pages
...sec (180° — b) = __losb = —sec b, (49) cosec (180° — 6) = .* - = cosec b; (50) that is, <Ae sine and cosecant of the supplement of an angle are the same as those of the angle itself; and the cosine, tangent, cotangent, and secant are the negatives of those...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 504 pages
...b; (50) x ' sin bv ' that is, <Ae sine awe? cosecant of the supplement of an angle are the same as those of the angle itself; and the cosine, tangent, cotangent, and secant are the negatives of those of the angle. 78. It follows from the preceding article, that the sine and...
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