A Treatise on TrigonometryG.W. Jones, 1890 - 160 Seiten |
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Seite 1
... side opposite sides If a segment of a line be designated by two letters , that part of the line is meant that lies between the points marked by the letters ; and the direction of a segment is indicated SECTION PAGE Positive and negative ...
... side opposite sides If a segment of a line be designated by two letters , that part of the line is meant that lies between the points marked by the letters ; and the direction of a segment is indicated SECTION PAGE Positive and negative ...
Seite 18
... in extreme and mean ratio the greater segment is the side of a regular inscribed decagon hence find the functions of 18 ° and of 36 ° . § 2. RELATIONS OF FUNCTIONS OF A SINGLE ANGLE . 18 [ II , th . TRIGONOMETRIC FUNCTIONS .
... in extreme and mean ratio the greater segment is the side of a regular inscribed decagon hence find the functions of 18 ° and of 36 ° . § 2. RELATIONS OF FUNCTIONS OF A SINGLE ANGLE . 18 [ II , th . TRIGONOMETRIC FUNCTIONS .
Seite 43
... side of the page ; the other , greater than 45 ° , has its degrees at the bottom and minutes at the right side of the page . The names of functions standing at the < top . bottom . top bottom of a column If angles of both the go with ...
... side of the page ; the other , greater than 45 ° , has its degrees at the bottom and minutes at the right side of the page . The names of functions standing at the < top . bottom . top bottom of a column If angles of both the go with ...
Seite 45
... side . right minutes that lie opposite the function at the { E.g. , to take out nat - sin1.44098 : then..44098 stands under nat - sine and 26 ° and opposite 10 ' at the left , .. the angle sought is 26 ° 10 ' , or its supplement , 153 ...
... side . right minutes that lie opposite the function at the { E.g. , to take out nat - sin1.44098 : then..44098 stands under nat - sine and 26 ° and opposite 10 ' at the left , .. the angle sought is 26 ° 10 ' , or its supplement , 153 ...
Seite 51
... side , must be given . The following principles relating to right triangles are here restated for convenience of reference : 1. The square of the hypothenuse is the sum of the squares of the two sides . 2. The sum of the two oblique ...
... side , must be given . The following principles relating to right triangles are here restated for convenience of reference : 1. The square of the hypothenuse is the sum of the squares of the two sides . 2. The sum of the two oblique ...
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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.