Elements of Plane and Spherical Trigonometry with Logarithmic and Other Mathematical Tables and Examples of Their Use and Hints on the Art of Computation, Volumen1H. Holt, 1882 - 168 páginas |
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Página 46
... applying the equations ( 18 ) of § 29 ( Chap . II . ) . 4. By means of the addition theorem prove the equations sin ( a + B + y ) = sin a cos ẞ cos y + cos a sin ẞ cos y + cos a cos B sin y ― - sin a sin ẞ sin y ; cos ( a + B + y ) ...
... applying the equations ( 18 ) of § 29 ( Chap . II . ) . 4. By means of the addition theorem prove the equations sin ( a + B + y ) = sin a cos ẞ cos y + cos a sin ẞ cos y + cos a cos B sin y ― - sin a sin ẞ sin y ; cos ( a + B + y ) ...
Página 74
... - k α b - Applying this method to the problem under consideration , we find k = 118.796 feet ; m = 0.462 97 ; frontages of lots , 27.778 and 32.222 feet . CHAPTER VII . THE THEORY OF POLYGONS . 63. A 74 PLANE TRIGONOMETRY .
... - k α b - Applying this method to the problem under consideration , we find k = 118.796 feet ; m = 0.462 97 ; frontages of lots , 27.778 and 32.222 feet . CHAPTER VII . THE THEORY OF POLYGONS . 63. A 74 PLANE TRIGONOMETRY .
Página 89
... applied to lines , express only the directions in which the lines are reckoned . By a change of direction the ... applying the algebraic signs will lead to the areas on the two sides of the point of crossing having opposite signs . Hence ...
... applied to lines , express only the directions in which the lines are reckoned . By a change of direction the ... applying the algebraic signs will lead to the areas on the two sides of the point of crossing having opposite signs . Hence ...
Página 102
... applying the forms ( 26 ) and ( 26 ′ ) alternately , and changing all the signs in ( 26 ) when an is odd , we find 30 or 22 sin ' x = - 2 cos 2x + 2 . 23 sin3 x = 2 ' sin3 x = - sin 3x + 3 sin - 3 sin ( -x ) + sin ( — 3x ) , x sin 3x3 ...
... applying the forms ( 26 ) and ( 26 ′ ) alternately , and changing all the signs in ( 26 ) when an is odd , we find 30 or 22 sin ' x = - 2 cos 2x + 2 . 23 sin3 x = 2 ' sin3 x = - sin 3x + 3 sin - 3 sin ( -x ) + sin ( — 3x ) , x sin 3x3 ...
Página 118
... applied generally in accordance with the following theorem : If we have found between the parts of a spherical triangle any equation which is true for all triangles , it will remain true when we permute the sides in any way ; provided ...
... applied generally in accordance with the following theorem : If we have found between the parts of a spherical triangle any equation which is true for all triangles , it will remain true when we permute the sides in any way ; provided ...
Términos y frases comunes
algebraic signs angle AOB angle XOM axes base circle circumference coefficients compute cos² cos³ cosec cosine cotangent distance divided equal example EXERCISES expression find the angles find the remaining find the values formulæ given gives Hence hypothenuse imaginary unit intersect latitude line OX measure metres negative nth roots obtain opposite angles parallel parallelogram perpendicular polar triangle pole polygon positive direction preceding problem quantities radius rectangular co-ordinates right angle right triangle roots of unity secant sin a cos sin a sin sin² sine sines and cosines Solution spherical triangle spherical trigonometry squares straight line substituting subtract supplementary angles suppose three angles three rectangular planes three sides tion trapezoid trigonometric functions trihedral angle vertex zero
Pasajes populares
Página 66 - In any triangle the square of any side is equal to the sum of the squares of the other two sides minus twice the product of these two sides and the cosine of their included angle.
Página 139 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Página 70 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Página 132 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts. II. The sine of the middle part is equal to the product of the cosines of the opposite parts.
Página 44 - To express the sine and cosine of the sum of two angles in terms of the sines and cosines of the angles.
Página 73 - If two triangles have two sides of the one respectively equal to two sides of the other, and the contained angles supplemental, the two triangles are equal.
Página 66 - IN any Obtuse-angled Triangle, the Square of the Side subtending the Obtuse Angle, is Greater than the Sum of the Squares of the other two Sides, by Twice the Rectangle of the Base and the Distance of the Perpendicular from the Obtuse Angle. Let ABC be a triangle...
Página 105 - ... the modulus of a product is equal to the product of the moduli of the factors.
Página 43 - At the top of a tower, 108 feet high, the angles of depression of the top and bottom of...
Página 73 - The area of a triangle is equal to half the product of any two of its sides multiplied by the sine of the included angle, radius being unity.