Elements of Plane and Spherical Trigonometry: With Their Applications to Heights and Distances Projections of the Sphere, Dialling, Astronomy, the Solution of Equations, and Geodesic OperationsBaldwin, Cradock, and Joy, 1816 - 244 páginas |
Dentro del libro
Resultados 1-5 de 10
Página 5
... cotangent of an arc or angle is the tangent of the complement of that arc or angle . The co - versed sine , and co - secant are de fined similarly . E M B T C D To exemplify these definitions by the annexed dia- gram : let AB be an ...
... cotangent of an arc or angle is the tangent of the complement of that arc or angle . The co - versed sine , and co - secant are de fined similarly . E M B T C D To exemplify these definitions by the annexed dia- gram : let AB be an ...
Página 6
... cotangent , and cм the cosecant , of the arc AB , or , by convention , of the angle ACB . Note . These terms are indicated by obvious con- tractions : Thus , for sine of the arc AB we use sin AB , tangent .... ditto ...... ditto ...
... cotangent , and cм the cosecant , of the arc AB , or , by convention , of the angle ACB . Note . These terms are indicated by obvious con- tractions : Thus , for sine of the arc AB we use sin AB , tangent .... ditto ...... ditto ...
Página 7
... cotangent , radius , and cosecant , constitute a third right angled triangle MEC , similar to both the preceding . Hence , when the sine and radius are known , the cosine is determined by Euc . i . 47. The same may be said of the ...
... cotangent , radius , and cosecant , constitute a third right angled triangle MEC , similar to both the preceding . Hence , when the sine and radius are known , the cosine is determined by Euc . i . 47. The same may be said of the ...
Página 15
... cotangent of half the sum of those two arcs , is to the catangent of half their difference . For , the cosines being the sines of the complements , it follows from the proposition that the sum of the co- sines , is to their difference ...
... cotangent of half the sum of those two arcs , is to the catangent of half their difference . For , the cosines being the sines of the complements , it follows from the proposition that the sum of the co- sines , is to their difference ...
Página 53
... cotangent of half the given angle , the sum will be the log . tangent of half the difference of the other two angles of the plane triangle . 38. Let us next return to the equation ( 1 ) in art . 11 of this chapter ; namely , a = b cos c ...
... cotangent of half the given angle , the sum will be the log . tangent of half the difference of the other two angles of the plane triangle . 38. Let us next return to the equation ( 1 ) in art . 11 of this chapter ; namely , a = b cos c ...
Otras ediciones - Ver todas
Términos y frases comunes
altitude angled spherical triangle axis azimuth base becomes bisect centre chap chord circle circle of latitude computation consequently cos² cosec cosine declination deduced determine dial diameter difference distance draw earth ecliptic equa equal equation Example find the rest formulæ given side h cos h half Hence horizon hour angle hour line hypoth hypothenuse intersecting latitude logarithmic longitude measured meridian oblique opposite angle parallel perpendicular plane angles plane triangle pole problem prop quadrant radius right angled spherical right angled triangle right ascension right line secant sin A sin sin² sine solid angle sphere spherical excess spherical trigonometry star substyle sun's supposed surface tan² tangent theorem three angles three sides tion triangle ABC values versed sine versin vertical angle whence zenith δα
Pasajes populares
Página 4 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.
Página 19 - In any plane triangle, as twice the rectangle under any two sides is to the difference of the sum of the squares of those two sides and the square of the base, so is the radius to the cosine of the angle contained by the two sides.
Página 30 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Página 251 - New General Atlas ; containing distinct Maps of all the principal States and Kingdoms throughout the World...
Página 69 - Being on a horizontal plane, and wanting to ascertain the height of a tower, standing on the top of an inaccessible hill, there were measured, the angle of elevation of the top of the hill 40°, and of the top of the tower 51° ; then measuring in a direct line 180 feet farther from the hill, the angle of elevation of the top of the tower was 33° 45' ; required the height of the tower.
Página 18 - AC, (Fig. 25.) is to their difference ; as the tangent of half the sum of the angles ACB and ABC, to the tangent of half their difference.
Página 85 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Página 19 - ... will be — As the base or sum of the segments Is to the sum of the other two sides, So is the difference of those sides To the difference of the segments of the base.
Página 70 - Required the horizontal distance of the mountain-top from the nearer station, and its height. Ans. Distance, 24840 yards; height, 1447 yards. 10. From the top of a light-house the angle of depression of a ship at anchor was observed to be 4° 52', from the bottom of the light-house the angle was 4° 2'.
Página 245 - XI- -A Treatise on Astronomy; in which the Elements of the Science are deduced in a natural Order, from the Appearances of the Heavens to an Observer on the Earth ; demonstrated on Mathematical Principles, and explained by an Application to the various Phenomena. By Olinthus Gregory, Teacher of Mathematics, Cambridge, 8vo.