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 11-15 de 63
Página 86
... equa ( 2 ) cos a = cos b cos c .... ( 6. ) For the same reason , the first of equa . ( 3 ) gives cos a sin B sin c = cos B COS C ; whence cos α = COS B COS C sin B sin c cot в cot c ( 7. ) .... Upon the same hypothesis , cot A becomes ...
... equa ( 2 ) cos a = cos b cos c .... ( 6. ) For the same reason , the first of equa . ( 3 ) gives cos a sin B sin c = cos B COS C ; whence cos α = COS B COS C sin B sin c cot в cot c ( 7. ) .... Upon the same hypothesis , cot A becomes ...
Página 89
... equa . ( 1 ) of this chapter ; from which we have sin c = sin csin B sin b sinc sinb ... sin c = sin B Case II . 33. Of these four things , viz . the three sides a , b , c , and an angle , any three being given , to find the fourth ...
... equa . ( 1 ) of this chapter ; from which we have sin c = sin csin B sin b sinc sinb ... sin c = sin B Case II . 33. Of these four things , viz . the three sides a , b , c , and an angle , any three being given , to find the fourth ...
Página 90
... equa . u ' ) , we have 1 + cos A = 2 cos2 A , and r Hence , 2 cos2 A = A COS A = 2 sin2 ža . cos acos b cos c sin b sin c + sin b sin c sin b sin c cos a cos ( b + c ) sin b sin c cos ( b - c ) cos a Hence also , 2 sin2 = sin b sin c ...
... equa . u ' ) , we have 1 + cos A = 2 cos2 A , and r Hence , 2 cos2 A = A COS A = 2 sin2 ža . cos acos b cos c sin b sin c + sin b sin c sin b sin c cos a cos ( b + c ) sin b sin c cos ( b - c ) cos a Hence also , 2 sin2 = sin b sin c ...
Página 91
... equa . ( 12 ) obviously reduces to • COS C = 1 tan b ' or cot cos ccot b ; which is analogous to equa . ( 8 ) . So that b is the hypothenuse and 4 one leg of a right angled triangle . The above transformation , therefore , is equivalent ...
... equa . ( 12 ) obviously reduces to • COS C = 1 tan b ' or cot cos ccot b ; which is analogous to equa . ( 8 ) . So that b is the hypothenuse and 4 one leg of a right angled triangle . The above transformation , therefore , is equivalent ...
Página 92
... equa . ( 15 ) is akin to equa . ( 8 ) ; showing that the operation here performed is equivalent to let- ting fall a perpendicular arc from the angle a to the base a ; the subsidiary arc being the segment adja- cent to the angle B. 2 ...
... equa . ( 15 ) is akin to equa . ( 8 ) ; showing that the operation here performed is equivalent to let- ting fall a perpendicular arc from the angle a to the base a ; the subsidiary arc being the segment adja- cent to the angle B. 2 ...
Otras ediciones - Ver todas
Términos y frases comunes
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