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 53
... equa . ( 3 ) -b tan ( A —B ) = a + b tan ( A + B ) tana- tan 45 ° 1 + tan a tan a -a - b a + b tan † ( A — B ) . whence cot & c tan ( AB ) cotic tan ( 45 ° ) .... ( 10. ) Hence results the following practical rule : - Subtract the less ...
... equa . ( 3 ) -b tan ( A —B ) = a + b tan ( A + B ) tana- tan 45 ° 1 + tan a tan a -a - b a + b tan † ( A — B ) . whence cot & c tan ( AB ) cotic tan ( 45 ° ) .... ( 10. ) Hence results the following practical rule : - Subtract the less ...
Página 54
... equa . ( 11 ) we substitute 1 2 sin2 A for ' Cos A , we shall have 2 sin1A = 1 + sin A - a2 - b2 - c2 ( a + b − c ) ... equa . ( 14 ) be divided by equa . ( 13 ) , there will result , tan A = -- [ † ( a + b + c ) — b ] . [ § ( a + b + c ) ...
... equa . ( 11 ) we substitute 1 2 sin2 A for ' Cos A , we shall have 2 sin1A = 1 + sin A - a2 - b2 - c2 ( a + b − c ) ... equa . ( 14 ) be divided by equa . ( 13 ) , there will result , tan A = -- [ † ( a + b + c ) — b ] . [ § ( a + b + c ) ...
Página 58
... - tural tangents are integers ? It is evident from equa . ( 4 ) that the sum of the three tangents must be equal to their continual product . Now , the only three integers which possess this property , are 58 Plane Trigonometry .
... - tural tangents are integers ? It is evident from equa . ( 4 ) that the sum of the three tangents must be equal to their continual product . Now , the only three integers which possess this property , are 58 Plane Trigonometry .
Página 60
... equa . ( 1 ) , sin 2A = 2 cos A sin A = x + 4 1 / ( 3x2 — 12 ) • x + 1 → 2x + 2 = sin B. By equating these two values of sin B , we have x + 1 x - 1 = x + 4 x + ] ; whence x2 + 2x + 1 = x2 + 3x − 4 , and 5. The sides , therefore , of ...
... equa . ( 1 ) , sin 2A = 2 cos A sin A = x + 4 1 / ( 3x2 — 12 ) • x + 1 → 2x + 2 = sin B. By equating these two values of sin B , we have x + 1 x - 1 = x + 4 x + ] ; whence x2 + 2x + 1 = x2 + 3x − 4 , and 5. The sides , therefore , of ...
Página 85
... equa . ( 1 ) gives sin b = Hence , by substitution , sin B sin c sin c cos c sin a sin c cos a cOS B + Dividing by sin c we have , COS COS C sin c sin a = cos a cos B + But = tan ( chap . i . 19 ) . sin Therefore cot c sin a sin B - cos ...
... equa . ( 1 ) gives sin b = Hence , by substitution , sin B sin c sin c cos c sin a sin c cos a cOS B + Dividing by sin c we have , COS COS C sin c sin a = cos a cos B + But = tan ( chap . i . 19 ) . sin Therefore cot c sin a sin B - cos ...
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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