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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... and cosines of multiple arcs , 97. Powers of the cosine , 99. Powers of the sine , 101. Trigonometric forms of imaginary expressions , 104. Roots of unity , 108 . 61 75 91 PART II . SPHERICAL TRIGONOMETRY . CHAPTER I. FUNDAMENTAL ...
... and cosines of multiple arcs , 97. Powers of the cosine , 99. Powers of the sine , 101. Trigonometric forms of imaginary expressions , 104. Roots of unity , 108 . 61 75 91 PART II . SPHERICAL TRIGONOMETRY . CHAPTER I. FUNDAMENTAL ...
Página 27
... root is the only one we want . Hence We then find Hence sin 18 ° = √5-1 4 cos ' 18 ° radius ' · sin2 18 ° = 1 — sin2 18 ° . - cos 18 ° = √10 + 2√ 4 31. Angles corresponding to given trigono- metric functions . When the value of a ...
... root is the only one we want . Hence We then find Hence sin 18 ° = √5-1 4 cos ' 18 ° radius ' · sin2 18 ° = 1 — sin2 18 ° . - cos 18 ° = √10 + 2√ 4 31. Angles corresponding to given trigono- metric functions . When the value of a ...
Página 50
... root of both members , sin ' ‡ y − + = ± 0087 ; - 2 whence , by solving , 1+ cos y sin y = V ( 21 ) 2 Let our fourth problem be : Given , sin y ; In the equation Required , cosy . = 2 sin y cos y sin y by cosy we put sin y = √1 — cosy ...
... root of both members , sin ' ‡ y − + = ± 0087 ; - 2 whence , by solving , 1+ cos y sin y = V ( 21 ) 2 Let our fourth problem be : Given , sin y ; In the equation Required , cosy . = 2 sin y cos y sin y by cosy we put sin y = √1 — cosy ...
Página 105
... represented by reti , the result will be Hence : ( repin = pnendi The modulus of a power is equal to the corresponding power of the modulus of the root . The argument of the power is the argument of the TRIGONOMETRIC DEVELOPMENTS . 105.
... represented by reti , the result will be Hence : ( repin = pnendi The modulus of a power is equal to the corresponding power of the modulus of the root . The argument of the power is the argument of the TRIGONOMETRIC DEVELOPMENTS . 105.
Página 106
Simon Newcomb. The argument of the power is the argument of the root multi- plied by the index of the power . 87. Periodicity of the imaginary exponential . From the known equations ( § 24 ) cos ( p + 2π ) = cos P , sin ( p + 2π ) = sin ...
Simon Newcomb. The argument of the power is the argument of the root multi- plied by the index of the power . 87. Periodicity of the imaginary exponential . From the known equations ( § 24 ) cos ( p + 2π ) = cos P , sin ( p + 2π ) = sin ...
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.