A Treatise on TrigonometryG.W. Jones, 1890 - 160 Seiten |
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Seite 58
... LAW OF SINES . THEOR . 2. In any plane triangle ABC For a : b : csin A : sin B : sin c ; draw DC ordinate of c as to AB ; b b α α then and ... So α ¦ c - q զ с DC B A QB D D Ac - q B [ df . sin . DC = AC sin a = b sin a , DC = BC sin ...
... LAW OF SINES . THEOR . 2. In any plane triangle ABC For a : b : csin A : sin B : sin c ; draw DC ordinate of c as to AB ; b b α α then and ... So α ¦ c - q զ с DC B A QB D D Ac - q B [ df . sin . DC = AC sin a = b sin a , DC = BC sin ...
Seite 59
... law of sines [ cr . 1 * GEOMETRIC PROOF . In the figure of cr . 1 draw DF parallel to EA and therefore perpendicular to AD ; then tan ( A — B ) = DF DF EA BD = cotc = AD EA AD BE a - b a + b cotc . EXAMPLES . 1 ... 4 . In any plane ...
... law of sines [ cr . 1 * GEOMETRIC PROOF . In the figure of cr . 1 draw DF parallel to EA and therefore perpendicular to AD ; then tan ( A — B ) = DF DF EA BD = cotc = AD EA AD BE a - b a + b cotc . EXAMPLES . 1 ... 4 . In any plane ...
Seite 105
... LAW OF SINES . THEOR . 8. In any spherical triangle ABC sin a sin b : sin c = sin a : sin B : sin c . For , draw DC arc - ordinate of c as to AB , then sin p = sin b sin a , and let p = DC ; [ fig . page 104 [ th . 4 and So .. sin p ...
... LAW OF SINES . THEOR . 8. In any spherical triangle ABC sin a sin b : sin c = sin a : sin B : sin c . For , draw DC arc - ordinate of c as to AB , then sin p = sin b sin a , and let p = DC ; [ fig . page 104 [ th . 4 and So .. sin p ...
Seite 106
... law of sines [ law of cosines [ add .. ( cos a + cos b ) ( 1 — cos c ) = k sin c sin ( A + B ) = ( sina sin b ) : ( sin A ± sin B ) . sin c sin ( A + B ) , ... ( sin a ± sin b ) : ( cos a + cos b ) = ( sin A ± sin B ) : sin ( A + B ) ...
... law of sines [ law of cosines [ add .. ( cos a + cos b ) ( 1 — cos c ) = k sin c sin ( A + B ) = ( sina sin b ) : ( sin A ± sin B ) . sin c sin ( A + B ) , ... ( sin a ± sin b ) : ( cos a + cos b ) = ( sin A ± sin B ) : sin ( A + B ) ...
Seite 109
... law of sines There is always one triangle , and but one ; the parts B , C are found without ambiguity by the formulæ , and by th . 9 cr . 1 , and the species of a is determined by Napier's analogies . ( b ) Given B , C , a , two angles ...
... law of sines There is always one triangle , and but one ; the parts B , C are found without ambiguity by the formulæ , and by th . 9 cr . 1 , and the species of a is determined by Napier's analogies . ( b ) Given B , C , a , two angles ...
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Häufige Begriffe und Wortgruppen
abscissa algebraic arc-ordinate area swept axis celestial sphere centre circle computation cos² cosc cosecant cosp cot Q cotangent difference of latitude difference of longitude direction draw ecliptic equal equator formulæ formulæ of th geom horizon hour-angle hypothenuse law of sines let xop log-cot log-sin logarithmic meridian miles nat-sin nearer right negative angle oblique angle oblique triangle observer's obtuse opposite ordinate perpendicular plane angle plane sailing polar pole positive and less positive angle possible errors prime vertical PROB projection quarter radians radius ratios right angles right ascension right spherical triangle right triangles sailing secant segment side sin b sin sin² Solve species straight line subtended sun's tan² tangent terminal line thence THEOR theorem triangle ABC trigonometric functions values vertex vertical angle wherein
Beliebte Passagen
Seite 126 - There are in general use three different kinds of time, True Solar Time — also called Apparent Solar Time — Mean Solar Time, and Sidereal Time. True or Apparent Solar Time is measured by the diurnal motion of the Sun, the length of the day being the interval between two successive transits of the Sun over the same meridian, and the time of day being the hour-angle of the Sun westward from the meridian. Owing to the obliquity of the ecliptic and to the lack of uniformity of the motion of the Earth...
Seite 121 - As to the horizon : The altitude of a star is its angular distance from the horizon measured on a vertical circle ; and the arc of the horizon intercepted between this circle and the south point of the horizon is the star's azimuth. Owing to the rotation of the celestial sphere, the horizon-coordinates change every moment.
Seite 10 - The radian is the plane angle with its vertex at the center of a circle that is subtended by an arc equal in length to the radius.
Seite 75 - Two observers on the same side of a balloon, and in the same vertical plane with it, are a mile apart, and find the angles of elevation to be 17° and 68° 25' respectively : what is its height ? [1836 feet.
Seite 107 - The law of sines states that in any spherical triangle the sines of the sides are proportional to the sines of their opposite angles: sin a _ sin b __ sin c _ sin A sin B sin C...
Seite 88 - Each angle of a spherical triangle is greater than the difference between two right angles and the sum of the other two angles.
Seite 73 - A wall is surrounded by a ditch ; from the edge of this ditch the angle of elevation of a point on the top of the wall is found to be 35° ; and at a distance of 100 yards from the ditch the angle of elevation of the same point...
Seite 20 - If the radius of a circle be divided in extreme and mean ratio, the greater segment is equal to one side of a regular inscribed decagon.
Seite 104 - ... cos a = cos b cos с + sin b sin с cos A ; (2) cos b = cos a cos с + sin a sin с cos в ; ^ A. (3) cos с = cos a cos b + sin a sin b cos C.
Seite 42 - C = 1 + 4 sin £A sin £B sin £C. 37. tan A + tan B + tan C = tan A tan B tan C.