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 3
... suppose , indif- ferently , Angle AOB = or Angle AOB = or Angle AOB = etc. angle - arc ab , angle - arc ab + 360 ° , angle - arc ab + 720 ° , etc. If we put C for 360 ° , or the circum- ference , the general measure of the angle is ...
... suppose , indif- ferently , Angle AOB = or Angle AOB = or Angle AOB = etc. angle - arc ab , angle - arc ab + 360 ° , angle - arc ab + 720 ° , etc. If we put C for 360 ° , or the circum- ference , the general measure of the angle is ...
Página 4
... suppose a distinction between the side from which we measure and the side to which we measure . In all the preceding examples we have supposed the measure to be from OA to OB . Had we measured from OB to OA , the arc ab would have been ...
... suppose a distinction between the side from which we measure and the side to which we measure . In all the preceding examples we have supposed the measure to be from OA to OB . Had we measured from OB to OA , the arc ab would have been ...
Página 11
... suppose OB , the side to which we measure ; M , the point in which OB intersects the circle ; XQ , the line tangent to the circle at X ; N , the point at which this tangent meets the side OB ; MP , the perpendicu- lar from M upon OX ...
... suppose OB , the side to which we measure ; M , the point in which OB intersects the circle ; XQ , the line tangent to the circle at X ; N , the point at which this tangent meets the side OB ; MP , the perpendicu- lar from M upon OX ...
Página 15
... suppose the revolving side OM to be produced indefi- nitely in both directions , and XO to be produced so as to form the diameter XU . Then , however the side OM may revolve- I. The sine of the angle XOM is always represented by the ...
... suppose the revolving side OM to be produced indefi- nitely in both directions , and XO to be produced so as to form the diameter XU . Then , however the side OM may revolve- I. The sine of the angle XOM is always represented by the ...
Página 16
... suppose the side Om of the angle XOm to revolve around 0 , carrying the sine mp with it , the latter will increase to its maximum value , equal to radius unity , when m reaches Y , and angle XOm = 90 ° . Hence sin 90 ° = +1 . As m moves ...
... suppose the side Om of the angle XOm to revolve around 0 , carrying the sine mp with it , the latter will increase to its maximum value , equal to radius unity , when m reaches Y , and angle XOm = 90 ° . Hence sin 90 ° = +1 . As m moves ...
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.