Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious Notes and IllustrationsA. Constable & Company, 1817 - 432 Seiten |
Im Buch
Ergebnisse 6-10 von 42
Seite 231
... sine and cosine of the arc AB , CF and OF the sine and cosine of BC , and CE is the sine of the compound arc AC . Consequently , R sin AC sin AB cos BC + cos AB sin BC . Cor . 1. Hence , likewise , the rectangle under TRIGONOMETRY . 231 ...
... sine and cosine of the arc AB , CF and OF the sine and cosine of BC , and CE is the sine of the compound arc AC . Consequently , R sin AC sin AB cos BC + cos AB sin BC . Cor . 1. Hence , likewise , the rectangle under TRIGONOMETRY . 231 ...
Seite 232
... sine of the difference of two arcs , is equal to the difference of the rectangles under their alternate sines and cosines ; or R sinAC'sin AB cosBC - cos AB sinBC . Cor . 2. If the two arcs A and B be equal , it is obvious that R sin2A ...
... sine of the difference of two arcs , is equal to the difference of the rectangles under their alternate sines and cosines ; or R sinAC'sin AB cosBC - cos AB sinBC . Cor . 2. If the two arcs A and B be equal , it is obvious that R sin2A ...
Seite 233
... sine of the mean arc . Let A - B , A , and A + B represent three arcs increasing by the difference B ; then R ( sin ( A + B ) + sin ( A — B ) ) = 2cosB sinA . 1 The property is easily deduced by combining the preced- TRIGONOMETRY . 233.
... sine of the mean arc . Let A - B , A , and A + B represent three arcs increasing by the difference B ; then R ( sin ( A + B ) + sin ( A — B ) ) = 2cosB sinA . 1 The property is easily deduced by combining the preced- TRIGONOMETRY . 233.
Seite 234
... sine of the common difference and the cosine of the mean arc ; or R ( sin ( A + B ) —sin ( A — B ) ) = 2sinB cosA . Cor . 2. Hence R ( cos ( A - B ) + cos ( A + B ) ) = 2cosB cos A , and R ( cos ( A - B ) —cos ( A + B ) ) = 2sinB sinA ...
... sine of the common difference and the cosine of the mean arc ; or R ( sin ( A + B ) —sin ( A — B ) ) = 2sinB cosA . Cor . 2. Hence R ( cos ( A - B ) + cos ( A + B ) ) = 2cosB cos A , and R ( cos ( A - B ) —cos ( A + B ) ) = 2sinB sinA ...
Seite 235
... sine of 30 ° being ( cor . 1. def . ) equal to the chord of 60 ° or the radius , it is evident that sin ( 60 ° + B ) ... sine of half the arc IAC ' , or of half the sum of the arcs AC and AC ' , as CF is the sine of half their differ- ence ...
... sine of 30 ° being ( cor . 1. def . ) equal to the chord of 60 ° or the radius , it is evident that sin ( 60 ° + B ) ... sine of half the arc IAC ' , or of half the sum of the arcs AC and AC ' , as CF is the sine of half their differ- ence ...
Inhalt
219 | |
225 | |
226 | |
231 | |
234 | |
237 | |
251 | |
256 | |
101 | |
110 | |
128 | |
142 | |
155 | |
181 | |
199 | |
200 | |
204 | |
257 | |
260 | |
262 | |
264 | |
283 | |
318 | |
338 | |
360 | |
365 | |
Andere Ausgaben - Alle anzeigen
Elements of Geometry, and Plane Trigonometry: With an Appendix, and Very ... University Professor Emeritus John Leslie, Sir Keine Leseprobe verfügbar - 2016 |
Häufige Begriffe und Wortgruppen
ABCD adjacent angle altitude angle ABC angle ADB angle BAC base AC bisect centre chord circle circumference consequently construction contained angle cosine decagon denote describe diameter difference distance diverging lines divided draw equal to BC equilateral triangle equivalent to twice evidently exterior angle given greater half Hence hypotenuse inscribed isosceles triangle join let fall likewise measure parallel perpendicular point G polygon PROB PROP Proposition quadrilateral figure quantities radius ratio rectangle rectangle contained rectilineal figure rhomboid right angles right-angled triangle Scholium segments semicircle semiperimeter sequently side AC sinB sine square of AB square of AC straight line tangent THEOR tion triangle ABC twice the rectangle twice the square vertex vertical angle whence Wherefore