A Treatise on TrigonometryG.W. Jones, 1890 - 160 Seiten |
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Seite 57
James Edward Oliver. § 4. GENERAL PROPERTIES OF PLANE TRIANGLES . LAW OF COSINES . THEOR . 1. In any plane triangle ABC b2 + c2 - a2 COS A = COS B = 2 bc c2 + a2 - b2 2 ca a2 + b2 - c2 COS C = 2 ab For , drop a perpendicular p from c to ...
James Edward Oliver. § 4. GENERAL PROPERTIES OF PLANE TRIANGLES . LAW OF COSINES . THEOR . 1. In any plane triangle ABC b2 + c2 - a2 COS A = COS B = 2 bc c2 + a2 - b2 2 ca a2 + b2 - c2 COS C = 2 ab For , drop a perpendicular p from c to ...
Seite 102
James Edward Oliver. § 5. GENERAL PROPERTIES OF SPHERICAL TRIANGLES . LAW OF COSINES . THEOR . 6. In any spherical triangle ABC , cos a = cos b cos c + sin b sin c cos A , ... b α c - q b с c - q q For , draw DC arc - ordinate of c as to ...
James Edward Oliver. § 5. GENERAL PROPERTIES OF SPHERICAL TRIANGLES . LAW OF COSINES . THEOR . 6. In any spherical triangle ABC , cos a = cos b cos c + sin b sin c cos A , ... b α c - q b с c - q q For , draw DC arc - ordinate of c as to ...
Seite 106
... cos a and i.e. , = ( sin a ± sin b ) : ( sin a ± sin B ) ; = cos b cos c = sin b sin c cos A = k sin c cos A sin B , cos b- cos a cos c = sin a sin c cos B = k sin c sin A COS B , - = - [ law of sines [ law of cosines [ add .. ( cos a + cos ...
... cos a and i.e. , = ( sin a ± sin b ) : ( sin a ± sin B ) ; = cos b cos c = sin b sin c cos A = k sin c cos A sin B , cos b- cos a cos c = sin a sin c cos B = k sin c sin A COS B , - = - [ law of sines [ law of cosines [ add .. ( cos a + cos ...
Seite 156
... cosines , 145 . of natural tangents , cotangents , secants , and cosecants , 147 . verification of , 146 . Congruent ... Cosine , see functions . computation of , 145 , 147 . definition of , 14 . law of , 57 , 102 . value of , in terms ...
... cosines , 145 . of natural tangents , cotangents , secants , and cosecants , 147 . verification of , 146 . Congruent ... Cosine , see functions . computation of , 145 , 147 . definition of , 14 . law of , 57 , 102 . value of , in terms ...
Seite 158
... law of cosines , 57 . law of sines , 58 . general properties of , 57 . examples of , 59 . solution of isosceles , 53 . of oblique , by right triangles , 53 . by general properties , 60 . of right , 51 . examples of , 53 , 54 . tangent ...
... law of cosines , 57 . law of sines , 58 . general properties of , 57 . examples of , 59 . solution of isosceles , 53 . of oblique , by right triangles , 53 . by general properties , 60 . of right , 51 . examples of , 53 , 54 . tangent ...
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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.