An Elementary Treatise of Spherical Geometry and TrigonometryDurrie & Peck, 1848 - 122 Seiten |
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Seite 59
... sin a : R :: sin b : sin B ; hence if unity be put for R , ( 1 ) sin b sin a sin B. Likewise , since the same equation holds good in the complemental triangles , sin b ' sin a ' sin B ' ; from which equation are derived the two ...
... sin a : R :: sin b : sin B ; hence if unity be put for R , ( 1 ) sin b sin a sin B. Likewise , since the same equation holds good in the complemental triangles , sin b ' sin a ' sin B ' ; from which equation are derived the two ...
Seite 60
... b tan C tan c ' sin b ' tan C ' = ( 2 ) cot a = cos C cot b ( 3 ) cot B = cos a tan C. 7. If of the sides and angles in a right 60 SPHERICAL TRIGONOMETRY .
... b tan C tan c ' sin b ' tan C ' = ( 2 ) cot a = cos C cot b ( 3 ) cot B = cos a tan C. 7. If of the sides and angles in a right 60 SPHERICAL TRIGONOMETRY .
Seite 61
... b cos c ( 3 ) cot a = cos C cot b ( 4 ) sin b = sin a sin B ( 5 ) tan c = sin b tan C. ( 6 ) cos C = cos c sin B To these must be added four others ; for it is evident that there are two equations belonging to each of the last four ...
... b cos c ( 3 ) cot a = cos C cot b ( 4 ) sin b = sin a sin B ( 5 ) tan c = sin b tan C. ( 6 ) cos C = cos c sin B To these must be added four others ; for it is evident that there are two equations belonging to each of the last four ...
Seite 62
... sin a sin C ( 9 ) tan b = sin c tan B ( 10 ) cos B = cos b sin C. The relations of the quanti- ties concerned in the equa- tions may be seen more clearly by aid of the accompanying figure . B 8. The ten equations of the six cases of ...
... sin a sin C ( 9 ) tan b = sin c tan B ( 10 ) cos B = cos b sin C. The relations of the quanti- ties concerned in the equa- tions may be seen more clearly by aid of the accompanying figure . B 8. The ten equations of the six cases of ...
Seite 63
... sin b = sin B sin a ( for the cosine of the com- plement of an arc or angle is the sine of that arc or angle ) . Also ( 3 ) sin c = tan b cot B ( 4 ) sin c = sin a sin C ( 5 ) cos B = tan c cot a ( 6 ) cos B = cos b sin C RIGHT - ANGLED ...
... sin b = sin B sin a ( for the cosine of the com- plement of an arc or angle is the sine of that arc or angle ) . Also ( 3 ) sin c = tan b cot B ( 4 ) sin c = sin a sin C ( 5 ) cos B = tan c cot a ( 6 ) cos B = cos b sin C RIGHT - ANGLED ...
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An Elementary Treatise of Spherical Geometry and Trigonometry Anthony Dumond Stanley Keine Leseprobe verfügbar - 2015 |
An Elementary Treatise of Spherical Geometry and Trigonometry Anthony D. Stanley Keine Leseprobe verfügbar - 2017 |
Häufige Begriffe und Wortgruppen
a=cos AB+BC adjacent angle ABC angle ACB angle opposite B+sin B cot b=cos BC and B'C C+sin C=cos c=sin circle circumference comp complemental computed corresponding cos C+sin cos C=cos cosec cosine distance drawn equal spheres equal to A'B formulæ given gles Hence hypotenuse included angle intersection Let ABC lune measures middle Napier's rule Napier's theorem oblique angles opposite angles opposite side pole of AC polygon quadrant radii radius remaining sides right angles right-angled spherical triangle right-angled triangle severally equal side AC side opposite sides AB sides and angles sin A+B sin b sin sin BC sine of AC smaller sphere sphere whose center spherical angle spherical polygon spherical triangle supplements tangent tangent of half three quantities three sides tri-quadrantal triangle trian triangle ABC trigonometry unequal vertex whence wherefore x=cos x=tan
Beliebte Passagen
Seite 50 - ... fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...
Seite 106 - ... that the sine of half the sum of any two sides of a spherical triangle, is to the sine of half their difference as the cotangent of half the angle contained between them, to the tangent of half the difference of the angles opposite to them : and also that the cosine of half the sum of these sides, is to the cosine of half their difference, as the cotangent of half the angle contained...
Seite 94 - 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...
Seite 96 - Spherical Triangle the cosine of any side is equal to the product of the cosines of the other two sides...
Seite 8 - Axis of a great circle of a sphere is that diameter of the sphere which is perpendicular to the plane of the circle.
Seite 27 - Therefore, if two triangles have two sides and the included angle of one, equal to two sides and the included angle of the other, the two triangles are equal in all respects.
Seite 101 - Law: cos a = cos b cos c + sin b sin c cos A cos b = cos c cos a + sin c sin a cos B cos c = cos a cos b + sin a sin b cos C cos A = -cos B...
Seite 96 - B . sin c = sin b . sin C cos a = cos b . cos c + sin b . sin c cos b = cos a . cos c + sin a . sin c cos A cos B cos c = cos a . cos b + sin a . sin b . cos C ..2), cotg b . sin c = cos G.
Seite 27 - If two angles of a spherical triangle are equal, the sides opposite these angles are equal and the triangle is isosceles. In the spherical triangle ABC, let the angle B equal the angle C. To prove that AC = AB. Proof. Let the A A'B'C
Seite 74 - Given two sides, and an angle opposite one of them, to find the remaining parts. 19. For this case, we employ proportions (3); sin a : sin b : : sin A .Ex. 1. Given the side a = 44° 13• 45", b = 84° 14• 29", and the angle A = 32° 26• 07" : required the remaining paris.