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 20
... determined by subtracting it from 90 ° , we can always find the sine , tangent , and secant of the complement when we know the angle . Therefore the sine , tangent , and secant of the comple- ment of an angle may be regarded as three ...
... determined by subtracting it from 90 ° , we can always find the sine , tangent , and secant of the complement when we know the angle . Therefore the sine , tangent , and secant of the comple- ment of an angle may be regarded as three ...
Página 27
... has equal values for positive and negative angles . Hence if a be an angle corresponding to a given cosine , a or 360 ° - a will equally correspond to it . - Hence when an angle is determined by its cosine , THE TRIGONOMETRIC FUNCTIONS .
... has equal values for positive and negative angles . Hence if a be an angle corresponding to a given cosine , a or 360 ° - a will equally correspond to it . - Hence when an angle is determined by its cosine , THE TRIGONOMETRIC FUNCTIONS .
Página 28
... determined , like the tangent , by the intersection of the revolving side with a tangent line , every pair of angles corresponding to the same tangent will also correspond to the same cotangent . Hence a and 180 ° + a always have the ...
... determined , like the tangent , by the intersection of the revolving side with a tangent line , every pair of angles corresponding to the same tangent will also correspond to the same cotangent . Hence a and 180 ° + a always have the ...
Página 30
... determined , by constructions like those of § 19. Knowing the angle , the values of the other functions can be found . Hence from any one func- tion of an angle all the others can be found . We have now to investigate the algebraic ...
... determined , by constructions like those of § 19. Knowing the angle , the values of the other functions can be found . Hence from any one func- tion of an angle all the others can be found . We have now to investigate the algebraic ...
Página 41
... distances AP and CP ? == What will be the distance if AC 80 yards and a = 85 ° 22′.5 ? 6. An engineer , desiring to determine the height of a vertical wall , measured off a distance P06 feet on level OF RIGHT TRIANGLES . 41.
... distances AP and CP ? == What will be the distance if AC 80 yards and a = 85 ° 22′.5 ? 6. An engineer , desiring to determine the height of a vertical wall , measured off a distance P06 feet on level OF RIGHT TRIANGLES . 41.
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.