A Treatise on TrigonometryG.W. Jones, 1890 - 160 Seiten |
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Seite 20
... formulæ , taken two and two , are symmetric . E.g. , those for sine , in ... The formulæ may also be proved by a geometric method . ... E.g. , if cot be given : take as linear unit the consequent of the ... th . TRIGONOMETRIC FUNCTIONS .
... formulæ , taken two and two , are symmetric . E.g. , those for sine , in ... The formulæ may also be proved by a geometric method . ... E.g. , if cot be given : take as linear unit the consequent of the ... th . TRIGONOMETRIC FUNCTIONS .
Seite 34
... the great im- portance of th . 11 , he should write out each of the four equa- tions involved , so that it may stand out clearly by itself ; and he should translate these equations into words and commit them to memory . This suggestion ...
... the great im- portance of th . 11 , he should write out each of the four equa- tions involved , so that it may stand out clearly by itself ; and he should translate these equations into words and commit them to memory . This suggestion ...
Seite 54
... the right triangles as before . ANGLES NEAR 90 ° OR NEAR 0 ° . 1. If P be near 90 ° , use the formulæ below . - tan P = √ [ ( r− q ) : ( r + q ) ] , p = ( r + q ) tan P. [ II th . 14 The formulæ assume that q , r are given ; but if p ...
... the right triangles as before . ANGLES NEAR 90 ° OR NEAR 0 ° . 1. If P be near 90 ° , use the formulæ below . - tan P = √ [ ( r− q ) : ( r + q ) ] , p = ( r + q ) tan P. [ II th . 14 The formulæ assume that q , r are given ; but if p ...
Seite 60
... formula of ths . 1 , 2 as serve to express the value of each of the three unknown parts in terms of three known ... th . 2 The formulæ give one value , and but one , for each part . ( b ) Given a , b , c , two sides and the included ...
... formula of ths . 1 , 2 as serve to express the value of each of the three unknown parts in terms of three known ... th . 2 The formulæ give one value , and but one , for each part . ( b ) Given a , b , c , two sides and the included ...
Seite 61
James Edward Oliver. In the limited triangle the formulæ give one value , and but one , for each part . ( c ) Given a , b , c , the three sides : Apply the formulæ of th . 1 . 1 In the limited triangle the formulæ give one value , and ...
James Edward Oliver. In the limited triangle the formulæ give one value , and but one , for each part . ( c ) Given a , b , c , the three sides : Apply the formulæ of th . 1 . 1 In the limited triangle the formulæ give one value , and ...
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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
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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.