A Treatise on TrigonometryG.W. Jones, 1890 - 160 Seiten |
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Seite 7
... subtends it . m +++ E.g. , Zlm is the angle from the line 7 to the line m . So , if ox , op be the initial and terminal lines , the angle is designated by XOP . Conversely , if an angle be designated by xoP , then ox , OP are the ...
... subtends it . m +++ E.g. , Zlm is the angle from the line 7 to the line m . So , if ox , op be the initial and terminal lines , the angle is designated by XOP . Conversely , if an angle be designated by xoP , then ox , OP are the ...
Seite 8
... subtended by an arc equal in length to the radius of the circle . This angle , being subtended by a radius - arc , is called a radian ; and since the half - circle contains radius - arcs , a radian is a th part of two right angles , and ...
... subtended by an arc equal in length to the radius of the circle . This angle , being subtended by a radius - arc , is called a radian ; and since the half - circle contains radius - arcs , a radian is a th part of two right angles , and ...
Seite 9
... subtending it to the radius of the eircle , i.e. , by the number of radii in the arc . 2. Express in degree - measure ... subtended by an arc of 5.71 in . , find : the radius ; the arcs opposite " , 1 " , 5 ° ; the angles in radians and ...
... subtending it to the radius of the eircle , i.e. , by the number of radii in the arc . 2. Express in degree - measure ... subtended by an arc of 5.71 in . , find : the radius ; the arcs opposite " , 1 " , 5 ° ; the angles in radians and ...
Seite 10
... subtended by : 2 radius - arcs , radius - arcs , 3 quadrants ? 10. How many radians in 17 ° 13 ' 15 " , 10 ° , 2009 ? 11. Convert into grades , minutes , and seconds : 1 ' , 86 ° 13 ′ 17 ′′ . 13. An angle of three radians at the centre ...
... subtended by : 2 radius - arcs , radius - arcs , 3 quadrants ? 10. How many radians in 17 ° 13 ' 15 " , 10 ° , 2009 ? 11. Convert into grades , minutes , and seconds : 1 ' , 86 ° 13 ′ 17 ′′ . 13. An angle of three radians at the centre ...
Seite 72
... equatorial radius 3962.76 miles , and the angle this radius subtends at the sun , 8 " .81 ; find the distance of the earth from the sun . [ 92,780,000 miles nearly . 10. How far should a coin an inch in diameter 72 [ III , PLANE TRIANGLES .
... equatorial radius 3962.76 miles , and the angle this radius subtends at the sun , 8 " .81 ; find the distance of the earth from the sun . [ 92,780,000 miles nearly . 10. How far should a coin an inch in diameter 72 [ III , PLANE TRIANGLES .
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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.