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 6
... dividing by CA , there results arc AB less than tangent AT . In a similar way it may be seen that chord AB , is less than arc AB , and sine BD , less than chord AB . The same is also evident from the consideration that a right line AB ...
... dividing by CA , there results arc AB less than tangent AT . In a similar way it may be seen that chord AB , is less than arc AB , and sine BD , less than chord AB . The same is also evident from the consideration that a right line AB ...
Página 35
... dividing each of these by the base , we shall have the tangent and A secant of A , respectively , to radius 1. Tracing in like manner , the consequences of assuming BC , and Ac , each for radius , we shall readily obtain these ...
... dividing each of these by the base , we shall have the tangent and A secant of A , respectively , to radius 1. Tracing in like manner , the consequences of assuming BC , and Ac , each for radius , we shall readily obtain these ...
Página 46
... dividing the two terms of the second member of the equation by cos a cos B , and recollecting that tan A = sin A COS A we shall obtain , ཉིན tan ( A + B ) * tan Atan B 1 tan a lan B ... ( 0 . ) If A in this formula be 45 ° , we shall ...
... dividing the two terms of the second member of the equation by cos a cos B , and recollecting that tan A = sin A COS A we shall obtain , ཉིན tan ( A + B ) * tan Atan B 1 tan a lan B ... ( 0 . ) If A in this formula be 45 ° , we shall ...
Página 47
... dividing the first values of sin A , cos A ( formula N ) one by the other , there will result , T COS A -COS A tan A = = + cos A sin A ( R. ) Thus tan 30 ° = - cos 60 ° sin 60 ° √3 √3 ; and tan 15 ° = 1 cos 30 ° = sia 30 ° = 2 -- and ...
... dividing the first values of sin A , cos A ( formula N ) one by the other , there will result , T COS A -COS A tan A = = + cos A sin A ( R. ) Thus tan 30 ° = - cos 60 ° sin 60 ° √3 √3 ; and tan 15 ° = 1 cos 30 ° = sia 30 ° = 2 -- and ...
Página 49
... dividing the sum of these by 2-1 , there results the following expression for the sine of any multiple arc ; viz . - ( cos A + sin A √ / — 1 ) " — ( co3 A — sin a√ — 1 ) " , - sin na = 21 I An analogous process will give $ ( cos A + ...
... dividing the sum of these by 2-1 , there results the following expression for the sine of any multiple arc ; viz . - ( cos A + sin A √ / — 1 ) " — ( co3 A — sin a√ — 1 ) " , - sin na = 21 I An analogous process will give $ ( cos A + ...
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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