A Treatise on TrigonometryG.W. Jones, 1890 - 160 Seiten |
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Seite v
... out for himself . These examples serve also a more important purpose : No real mastery of any mathematical subject can be got . by merely reading demonstrations and solving illustrative numerical examples . PREFACE . V.
... out for himself . These examples serve also a more important purpose : No real mastery of any mathematical subject can be got . by merely reading demonstrations and solving illustrative numerical examples . PREFACE . V.
Seite vi
... solving quite as much as upon the reading of the text , the authors have sought to lay out such work as is most important and most instructive , with only so much of guidance as shall make it easy and attractive . CONTENTS . SECTION I ...
... solving quite as much as upon the reading of the text , the authors have sought to lay out such work as is most important and most instructive , with only so much of guidance as shall make it easy and attractive . CONTENTS . SECTION I ...
Seite 21
... = tan3 0+ cot3 0 . = 2 vers vers2 0 . - 8 ... 12 . Solve the equations : 8. sin cos 0 : = 1 . 9. 3 sin 0+ 4 cos 0 = 5 . 10. tan + cot 0 = 2 . 11. cot 0 = 2 cos 0 . 12. 2 sin2 0 - 5 cos 0 = 4 4 , § 2. ] 21 FUNCTIONS OF A SINGLE ANGLE .
... = tan3 0+ cot3 0 . = 2 vers vers2 0 . - 8 ... 12 . Solve the equations : 8. sin cos 0 : = 1 . 9. 3 sin 0+ 4 cos 0 = 5 . 10. tan + cot 0 = 2 . 11. cot 0 = 2 cos 0 . 12. 2 sin2 0 - 5 cos 0 = 4 4 , § 2. ] 21 FUNCTIONS OF A SINGLE ANGLE .
Seite 22
... solve by direct reference to the formulæ , or , better , draw a right triangle two of whose lines are in the given ratio , compute the third line , and write down the other ratios . E.g. , if cos 0 = -4 : 5 ; with radius 5 and o as ...
... solve by direct reference to the formulæ , or , better , draw a right triangle two of whose lines are in the given ratio , compute the third line , and write down the other ratios . E.g. , if cos 0 = -4 : 5 ; with radius 5 and o as ...
Seite 36
... Solve the equations : cos 30+ cos 20+ cos 0 = 0 , sin - 13a + sin14 , tan - 12x + tan - 13x = 1 . 15. If A , B , C , D be any four plane angles , sin ( A - B ) sin ( C — D ) + sin ( B - C ) sin ( A - D ) + sin ( C - A ) sin ( B - D ) ...
... Solve the equations : cos 30+ cos 20+ cos 0 = 0 , sin - 13a + sin14 , tan - 12x + tan - 13x = 1 . 15. If A , B , C , D be any four plane angles , sin ( A - B ) sin ( C — D ) + sin ( B - C ) sin ( A - D ) + sin ( C - A ) sin ( B - D ) ...
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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.