The Theory of Navigation and Nautical Astronomy: Together with the Elements of Plane and Spherical Trigonometry, with Examples for the Use of Marine CadetsBell and Daldy, 1869 - 154 Seiten |
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Seite 7
... sin A = 1 . BC BC sin A AC CLASS III . Since in the triangle ABC , the angle B 90 ° .. A + C = 90 ° ( I. Euc . 32 ) .. C = ( 90 ° — A ) And sin A = AC BC cos C cos ( 90 ° — A ) - AB Also cos A = sin C sin ( 90 PLANE TRIGONOMETRY . 7.
... sin A = 1 . BC BC sin A AC CLASS III . Since in the triangle ABC , the angle B 90 ° .. A + C = 90 ° ( I. Euc . 32 ) .. C = ( 90 ° — A ) And sin A = AC BC cos C cos ( 90 ° — A ) - AB Also cos A = sin C sin ( 90 PLANE TRIGONOMETRY . 7.
Seite 8
... sin C sin ( 90 ° - A ) AC BC tan A = " " = cot C = cot ( 90 ° A ) AB AB cot A = " " = tan C = tan ( 90 ° - BC A ) AC ... cos B + ( 2 ) Cos ( A + B ) = cos A cos B ( 3 ) Sin ( AB ) = sin A. cos B ( 4 ) Cos ( A - cos A sin B - sin A sin B ...
... sin C sin ( 90 ° - A ) AC BC tan A = " " = cot C = cot ( 90 ° A ) AB AB cot A = " " = tan C = tan ( 90 ° - BC A ) AC ... cos B + ( 2 ) Cos ( A + B ) = cos A cos B ( 3 ) Sin ( AB ) = sin A. cos B ( 4 ) Cos ( A - cos A sin B - sin A sin B ...
Seite 20
... Cos A = b2 + c2 2 bc a2 Fig . 7 . α A D C 1st . When angle A , is acute . Let ABC be a plane triangle , whose sides are a , b , c , respectively . From C , draw CD at right angles to AB , Then by ( Euc . II . XIII ) , BC2 BA2 + AC2 or ...
... Cos A = b2 + c2 2 bc a2 Fig . 7 . α A D C 1st . When angle A , is acute . Let ABC be a plane triangle , whose sides are a , b , c , respectively . From C , draw CD at right angles to AB , Then by ( Euc . II . XIII ) , BC2 BA2 + AC2 or ...
Seite 22
... Sin A = b ) ( S bc b2 + c2 a2 Since cos A = 2bc Subtract both sides from 1 , then , 1- cos A = 1 - b2 + c2 2bc - b2 ― b2 2bc - 2bc - - a2 c2 + a2 c2 + 2b c 2bc ( b2 + c2 2bc -- c ) 2 - 2bc ) a2 a2 a2 ( b ( a + b - - c ) ( a b + c ) 2bc ...
... Sin A = b ) ( S bc b2 + c2 a2 Since cos A = 2bc Subtract both sides from 1 , then , 1- cos A = 1 - b2 + c2 2bc - b2 ― b2 2bc - 2bc - - a2 c2 + a2 c2 + 2b c 2bc ( b2 + c2 2bc -- c ) 2 - 2bc ) a2 a2 a2 ( b ( a + b - - c ) ( a b + c ) 2bc ...
Seite 23
... Sin A TanA = Cos A ( S — b ) ( S — c ) - Therefore Tan A = J S. ( S a ) ( Sb ) ( S — c ) S. ( S - a ) bc bc ( 7 ) The value of the sine of an angle in terms of the sides , or Sin A = 2S . ( Sa ) ( S — b ) ( S — c ) bc Since Sin 2 A = 2 ...
... Sin A TanA = Cos A ( S — b ) ( S — c ) - Therefore Tan A = J S. ( S a ) ( Sb ) ( S — c ) S. ( S - a ) bc bc ( 7 ) The value of the sine of an angle in terms of the sides , or Sin A = 2S . ( Sa ) ( S — b ) ( S — c ) bc Since Sin 2 A = 2 ...
Häufige Begriffe und Wortgruppen
AC AC angle of elevation angled plane triangle angled spherical triangle Area Asin azimuth body celestial centre colatitude cos a cos cos(A cos(A+B cos² cosec cosine cot lat cotangent declination diff Earth ecliptic equal equator feet find AC find angles find the latitude formulæ given Greenwich height hence horizon hour angle limb log AC log cosec longitude measured meridian altitude NAUTICAL ASTRONOMY object observed parallax parallel sailing perpendicular plane sailing polar dist polar distance polar triangle pole prime vertical prove radius refraction right angled spherical right angled triangle sailing Secant sextant sin a sin sin A+B sin c cos sin² sine spherical triangle ABC Spherical Trigonometry star Subtract both sides Sun's tangent Vernier vers whence yards zenith distance Zs-Zm
Beliebte Passagen
Seite 2 - We have, then, that the sine of an angle is equal to the cosine of its complement, and conversely.
Seite 19 - Plane Triangle, As the Sum of any two Sides ; Is to their Difference ; So is the Tangent of half the Sum of the two opposite Angles ; To the Tangent of half the Difference between them.
Seite 113 - Is to the sum of the other two sides, So is the difference of those sides To the difference of the segments of the base.
Seite 25 - A straight line is perpendicular, or at right angles, to a plane, when it makes right angles with every straight line meeting it in that plane. 4. A plane is perpendicular...
Seite 8 - Formeln cos (a + b) = cos a cos b — sin a sin b, (2) cos (a — b) = cos a cos b + sin a sin b, (3...
Seite 42 - The sum of the three sides of a spherical triangle is less than the circumference of a great circle. Let ABC be any spherical triangle; produce the sides AB, AU, till they meet again in D.
Seite 26 - THEOREM. Every section of a sphere, made by a plane, is a circle.
Seite 128 - ... 24". Required their distance. Ans. 1090.85 yards. 9. From the top of a mountain, three miles in height, the visible horizon appeared depressed 2° 13
Seite 25 - The inclination of a plane to a plane is the acute angle contained by two straight lines drawn from any the...
Seite 25 - The sphere may be conceived to be generated by the revolution of a semicircle DAE...