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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Resultados 6-10 de 37
Página 40
... obtained . They may be placed to- gether , thus a = b cos c + c cos B ba cos c + c cos A ca cos B + b cos A ( 1. ) 12. If BC , or a , be regarded as radius , CD will be the sine of the angle в to that radius ; therefore , to the ra ...
... obtained . They may be placed to- gether , thus a = b cos c + c cos B ba cos c + c cos A ca cos B + b cos A ( 1. ) 12. If BC , or a , be regarded as radius , CD will be the sine of the angle в to that radius ; therefore , to the ra ...
Página 41
... obtain a or = a sin A = and - = с sin c ' b sin B с sin c Or , changing the denomina- tors , the relations of all the six quantities may be thus expressed , sin A sin B sin c ...... ... ( 2. ) a C These equations are , manifestly , of ...
... obtain a or = a sin A = and - = с sin c ' b sin B с sin c Or , changing the denomina- tors , the relations of all the six quantities may be thus expressed , sin A sin B sin c ...... ... ( 2. ) a C These equations are , manifestly , of ...
Página 43
... obtained , in which each quantity is expressed in terms of its own kind . sin A = S sin 2A = 2s - ( 1 — s2 ) ( 4s8s3 ) √ ( 1 — s2 ) sin 5A 5s 20s3 + 16s5 - 32s3 + 32s3 ) √ ( 1 − s2 ) sin 3A 3s 4s3 sin 4A = sin 6A = ( 6s & c . COS A ...
... obtained , in which each quantity is expressed in terms of its own kind . sin A = S sin 2A = 2s - ( 1 — s2 ) ( 4s8s3 ) √ ( 1 — s2 ) sin 5A 5s 20s3 + 16s5 - 32s3 + 32s3 ) √ ( 1 − s2 ) sin 3A 3s 4s3 sin 4A = sin 6A = ( 6s & c . COS A ...
Página 45
... the sum of all the natural cosines of every minute in the quadrant , gives sin 45 x cos 45 ° 0 ′ 30 ′′ sin 30 " 3437 2470374 . 23. Otherwise , in order to obtain expressions for the Analytical Investigation of Properties . 45.
... the sum of all the natural cosines of every minute in the quadrant , gives sin 45 x cos 45 ° 0 ′ 30 ′′ sin 30 " 3437 2470374 . 23. Otherwise , in order to obtain expressions for the Analytical Investigation of Properties . 45.
Página 46
... obtain expressions for the sine and cosine of a half arc , take 1 = cos 2A + sin 2A cos 2A = cos 2A - sin 2A ( see formulæ D ) , the sum and difference of these respectively , give 2 cos 2A = 1 + cos 2A , and 2 sin 2A = 1 Changing A and ...
... obtain expressions for the sine and cosine of a half arc , take 1 = cos 2A + sin 2A cos 2A = cos 2A - sin 2A ( see formulæ D ) , the sum and difference of these respectively , give 2 cos 2A = 1 + cos 2A , and 2 sin 2A = 1 Changing A and ...
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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