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 38
... soever are given , the remaining parts may be found by the equations ( 4 ) and ( 5 ) . The following are all the essentially different cases . 37. CASE I. Given the two sides a and b 38 PLANE TRIGONOMETRY . Solution of right triangles,
... soever are given , the remaining parts may be found by the equations ( 4 ) and ( 5 ) . The following are all the essentially different cases . 37. CASE I. Given the two sides a and b 38 PLANE TRIGONOMETRY . Solution of right triangles,
Página 39
... remaining parts of the triangle . Solution by numbers and measurement . tan α = = 0.75 . On the tangent line XN ( §22 ) measure a distance from X equal to 0.75 of the radius OX ; join the end of the distance to O , and measure the angle ...
... remaining parts of the triangle . Solution by numbers and measurement . tan α = = 0.75 . On the tangent line XN ( §22 ) measure a distance from X equal to 0.75 of the radius OX ; join the end of the distance to O , and measure the angle ...
Página 40
... remaining side is found by the equation = b = c cos α . Example . Given a 13 , c = 20 , to find the remaining parts . Solution by numbers and measurement . sin α = α 13 = с 20 = 0.65 . 0.65 of OX in the dividers , and find Take a ...
... remaining side is found by the equation = b = c cos α . Example . Given a 13 , c = 20 , to find the remaining parts . Solution by numbers and measurement . sin α = α 13 = с 20 = 0.65 . 0.65 of OX in the dividers , and find Take a ...
Página 41
... remaining parts . 66 b = c = 16 ; 66 66 ( 6 α = 82.143 , c = 120.412 ; 66 66 66 66 b = 2.9235 , c = 9.827 ; 66 66 66 4 . 5. A circle of radius r is drawn with its centre at a distance p from a straight line . What length will it cut out ...
... remaining parts . 66 b = c = 16 ; 66 66 ( 6 α = 82.143 , c = 120.412 ; 66 66 66 66 b = 2.9235 , c = 9.827 ; 66 66 66 4 . 5. A circle of radius r is drawn with its centre at a distance p from a straight line . What length will it cut out ...
Página 61
... remaining three may be found , but in order to be independent one of the three given parts must be a side . 55. The fact that the sum of the three angles of a plane triangle is 180 ° enables us to express a trigonometric function of any ...
... remaining three may be found , but in order to be independent one of the three given parts must be a side . 55. The fact that the sum of the three angles of a plane triangle is 180 ° enables us to express a trigonometric function of any ...
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.