The Elements of Plane and Spherical Trigonometry: And Its Application to Astronomy, Dialling, and Trigonometrical Surveying. With Plates. Designed for Mathematical StudentsT. Ostell and Company, 1841 - 191 sider |
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Resultat 1-5 av 32
Side 3
... known and constant , the angle is generally measured by the length of the intercepted arc described with the radius unity ; hence , by art . ( 2. ) , On this supposition , the right angle = arc radius angle , or 90 ° = 2 two right ...
... known and constant , the angle is generally measured by the length of the intercepted arc described with the radius unity ; hence , by art . ( 2. ) , On this supposition , the right angle = arc radius angle , or 90 ° = 2 two right ...
Side 27
... known by the application of principles , which constitute Plane Trigonometry . ( 47. ) Let A B C ( fig . 7. ) be a triangle , right angled at C ; and let the sides opposite to the angles A , B , C , be denoted by the small letters a , b ...
... known by the application of principles , which constitute Plane Trigonometry . ( 47. ) Let A B C ( fig . 7. ) be a triangle , right angled at C ; and let the sides opposite to the angles A , B , C , be denoted by the small letters a , b ...
Side 34
... a + b 2 a - b A - B tan 2 therefore , tan A - B a - b C ; and A + B and 2 cot ja 2 a + b 2 4 - B being known , their sum gives the 2 value of A , and their difference that of B. The third side ( c ) , may be determined 34 THE ELEMENTS OF.
... a + b 2 a - b A - B tan 2 therefore , tan A - B a - b C ; and A + B and 2 cot ja 2 a + b 2 4 - B being known , their sum gives the 2 value of A , and their difference that of B. The third side ( c ) , may be determined 34 THE ELEMENTS OF.
Side 36
... ( 57. ) The principles investigated in the foregoing articles , with the elementary equation A + B + C = ” , are sufficient for the solution of all plane triangles , H when any three parts are known . The case , 36 THE ELEMENTS OF.
... ( 57. ) The principles investigated in the foregoing articles , with the elementary equation A + B + C = ” , are sufficient for the solution of all plane triangles , H when any three parts are known . The case , 36 THE ELEMENTS OF.
Side 37
... known . The case , how- ever , must be excepted when the three angles only are given ; for then the ratio of the sides only be- comes known ( 48 ) . ( 58. ) There are cases to be considered , called the ambiguous cases , in which the ...
... known . The case , how- ever , must be excepted when the three angles only are given ; for then the ratio of the sides only be- comes known ( 48 ) . ( 58. ) There are cases to be considered , called the ambiguous cases , in which the ...
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The Elements of Plane and Spherical Trigonometry: And Its Application ... Richard Abbatt Ingen forhåndsvisning tilgjengelig - 2017 |
The Elements of Plane and Spherical Trigonometry: And Its Application ... Richard Abbatt Ingen forhåndsvisning tilgjengelig - 2018 |
Vanlige uttrykk og setninger
1+cos 1+tan A-sin A'+B A+B+C A+tan ab+cd angle of elevation Answer B-cos B-sin B+cos c-cos C-tan c=cos calculation called centre complement cos² cosec cosine cotangent determine diurnal motion earth ecliptic equal equation Example find the angle formulæ greater Greenwich hence horizon hour circle hypothenuse included angle known latitude less Let A B C log a log logarithms longitude measured meridian altitudes miles obliq obliquity observed perpendicular plane triangle polar triangle pole prime vertical Problem quadrant radius right ascension secant sides A B Similarly sin S-a sin² sine sine and cosine six o'clock sphere spherical angle spherical tri spherical triangle SPHERICAL TRIGONOMETRY subtraction Suppose surface tan² tangent third side three angles three sides Tobolsk triangle A B C TRIGONO trigonometrical lines vernal equinox yards
Populære avsnitt
Side 58 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.
Side 55 - From a window near the bottom of a house, which seemed to be on a level with the bottom of a steeple, I took the angle of elevation of the top of the steeple equal...
Side 31 - THEOREM I. The sides of a plane triangle are proportional to the sines of their opposite angles.
Side 66 - That is, the sines of the sides of a spherical triangle are proportional to the sines of the opposite angles.
Side 60 - A great circle may be drawn through any two points on the surface of a sphere, but not through more than two, taken at random.
Side 57 - Required the horizontal distance of the vessel, and the height of the promontory above the level of the sea, the light-house being 85 feet high. Ans. Distance 5296.4 feet, height 251.3 feet. Prob. 11. An observer, seeing a cloud in the west, measured its angle of elevation, and found it to be 64°. A second observer, situated half a mile due east from the first station, and on the same...
Side 54 - What is the perpendicular height of a hill ; its angle of elevation, taken at the bottom of it, being 46°, and 200 yards farther off, on a level with the bottom, the angle was 31°?
Side 57 - ... it is required from these measures to determine the magnitude of the whole earth, and the utmost distance that can be seen on its surface from the top of the mountain, supposing the form of the earth to be perfectly...
Side x - CB : CA : : sin A : sin B. For, with A as a centre, and AD equal to the less side...
Side 57 - Required the distance from A to B. Ans. 345.5 yards. Prob. 10. From the top of a light-house, the angle of depression of a ship at anchor was 3° 38', and at the bottom of the light-house the angle of depression was 2° 43'.