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 14
... parallel to OX , the point in which it intersects the arc will give the required angle . To find the angle corresponding to a given R S tangent we take a distance XS equal to the product of the given tangent into the radius . Join OS ...
... parallel to OX , the point in which it intersects the arc will give the required angle . To find the angle corresponding to a given R S tangent we take a distance XS equal to the product of the given tangent into the radius . Join OS ...
Página 17
... parallel to the tangent line , and the point N will recede to infinity . Hence : The tangent of 90 ° is infinite . X M Y X When m is in the second quadrant , suppose in the position M , the revolving side OM will not intersect the ...
... parallel to the tangent line , and the point N will recede to infinity . Hence : The tangent of 90 ° is infinite . X M Y X When m is in the second quadrant , suppose in the position M , the revolving side OM will not intersect the ...
Página 21
... parallel to OX . Then— IV . The cosine of any angle XOM is represented by the distance OP to the foot of the sine , positive or negative according to its direction . U X Р Р -T V. The cotangent of any angle XOM is represented by THE ...
... parallel to OX . Then— IV . The cosine of any angle XOM is represented by the distance OP to the foot of the sine , positive or negative according to its direction . U X Р Р -T V. The cotangent of any angle XOM is represented by THE ...
Página 69
... parallel sides of a trapezoid are 12 and 17 , and the non- parallel sides 6 and 7. Find its four angles . Suggestion . Divide the trapezoid into a triangle and a parallelogram . 7. In a triangle are given the two sides , p and q , and ...
... parallel sides of a trapezoid are 12 and 17 , and the non- parallel sides 6 and 7. Find its four angles . Suggestion . Divide the trapezoid into a triangle and a parallelogram . 7. In a triangle are given the two sides , p and q , and ...
Página 74
... parallel to AB . What will be the ratios of the segments into which the other two sides are divided ? Ans . 1 : 1– √§ . 8. A city lot fronts 60 feet on a street , and the parallel sides run back , the one 100 and the other 135 feet ...
... parallel to AB . What will be the ratios of the segments into which the other two sides are divided ? Ans . 1 : 1– √§ . 8. A city lot fronts 60 feet on a street , and the parallel sides run back , the one 100 and the other 135 feet ...
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.