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 |
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Página 7
... cosine , and radius . And , BD : BC : CE : CM ; that is , the cosecant is a third proportional to the sine and radius . ( H ) . Thus , employing the usual abbreviations , we should have 3. sec = 1. cos ( rad2- sin2 ) . Definitions . 7.
... cosine , and radius . And , BD : BC : CE : CM ; that is , the cosecant is a third proportional to the sine and radius . ( H ) . Thus , employing the usual abbreviations , we should have 3. sec = 1. cos ( rad2- sin2 ) . Definitions . 7.
Página 8
... sin2 ) . √ ( rad2 + tan2 ) . 5. tan = 7. sec = rad ' x sin COS rad2 COS • These , when unity is circle , become - 1. cos = √ ( 1 − sin2 ) . 3. sec = ( 1 + tan2 ) . 5. tan = sin COS • 6. cot = COS sin 2. tan = √ ( sec2 — rad2 ) . 4 ...
... sin2 ) . √ ( rad2 + tan2 ) . 5. tan = 7. sec = rad ' x sin COS rad2 COS • These , when unity is circle , become - 1. cos = √ ( 1 − sin2 ) . 3. sec = ( 1 + tan2 ) . 5. tan = sin COS • 6. cot = COS sin 2. tan = √ ( sec2 — rad2 ) . 4 ...
Página 17
... sin 2 ' , sin 59 ° 57 ′ + sin 3 ' , şin 64 ° 0 ′ = sin 56 ° 0 ′ + sin 4o , & c . & c . & c . PROP . XIII . 13. In any right angled triangle , the hypothenuse is to one of the legs , as the radius to the sine of the angle opposite to ...
... sin 2 ' , sin 59 ° 57 ′ + sin 3 ' , şin 64 ° 0 ′ = sin 56 ° 0 ′ + sin 4o , & c . & c . & c . PROP . XIII . 13. In any right angled triangle , the hypothenuse is to one of the legs , as the radius to the sine of the angle opposite to ...
Página 22
... ( sin2 ) . This theorem gives , in the pre- sent case , cos 1 ' = 9999999577 . Then , by prop . 12 , cor . 2 , ( A ) , of this chapter , we shall have sin 3 ′ -- 2 cos l ' x sin l'- 2 cos l ' x sin 2 ' 2 cos l'x 2 cos l ' x 2 cos l ' x ...
... ( sin2 ) . This theorem gives , in the pre- sent case , cos 1 ' = 9999999577 . Then , by prop . 12 , cor . 2 , ( A ) , of this chapter , we shall have sin 3 ′ -- 2 cos l ' x sin l'- 2 cos l ' x sin 2 ' 2 cos l'x 2 cos l ' x 2 cos l ' x ...
Página 23
... sin 2 ° :: sin 3 ° + sin 2 ° : sin . 5 ° sin 3 ° :: sin 4 ° + sin 3 ° : sin 7 ° sin 4o : sin 7 ° - sin 3 ° :: sin 7 ° + sin 3 ° : sin 10 ° . The coincidence of the results thus obtained , with the analogous results in the preceding ...
... sin 2 ° :: sin 3 ° + sin 2 ° : sin . 5 ° sin 3 ° :: sin 4 ° + sin 3 ° : sin 7 ° sin 4o : sin 7 ° - sin 3 ° :: sin 7 ° + sin 3 ° : sin 10 ° . The coincidence of the results thus obtained , with the analogous results in the preceding ...
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altitude angled spherical triangle azimuth base becomes bisect centre chap chord circle circle of latitude computation consequently cos² cosec cosine cotangent 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 hypoth hypothenuse intersecting latitude logarithmic longitude measured meridian obliq oblique opposite angle parallel perpendicular plane angles plane triangle pole problem prop quadrant radius right angled spherical right angled triangle right ascension right line sec² 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