Elements of Plane and Spherical Trigonometry with Logarithmic and Other Mathematical Tables and Examples of Their Use and Hints on the Art of ComputationH. Holt, 1882 - 104 páginas |
Dentro del libro
Resultados 6-10 de 75
Página 13
... equal to the products of the radius by the corresponding functions . For example , if sin XOM = PM Radius ' then sin XOM . Radius = PM . 18. Remark . The sine of an angle is equal to half the chord of twice the arc of the angle , the ...
... equal to the products of the radius by the corresponding functions . For example , if sin XOM = PM Radius ' then sin XOM . Radius = PM . 18. Remark . The sine of an angle is equal to half the chord of twice the arc of the angle , the ...
Página 14
... equal to the given sine , the radius being unity . y Therefore if we take on the perpendicular OY a distance OR equal to the product of the radius by the given sine , and through R draw a parallel to OX , the point in which it ...
... equal to the given sine , the radius being unity . y Therefore if we take on the perpendicular OY a distance OR equal to the product of the radius by the given sine , and through R draw a parallel to OX , the point in which it ...
Página 15
... equal lengths OX and OM as the unit of measurement and radius of the circle . At we erect a line TXT ' perpendicular to OX , extending indefinitely in both directions . We also suppose the revolving side OM to be produced indefi- nitely ...
... equal lengths OX and OM as the unit of measurement and radius of the circle . At we erect a line TXT ' perpendicular to OX , extending indefinitely in both directions . We also suppose the revolving side OM to be produced indefi- nitely ...
Página 16
... equal to radius unity , when m reaches Y , and angle XOm = 90 ° . Hence sin 90 ° +1 . As m moves from Y to X ' , the sine will diminish from 1 to zero . Because angle XOX ' = 180 ° , sin 180 ° = 0 . M m P ' X P P P X M M " Y ' If m ...
... equal to radius unity , when m reaches Y , and angle XOm = 90 ° . Hence sin 90 ° +1 . As m moves from Y to X ' , the sine will diminish from 1 to zero . Because angle XOX ' = 180 ° , sin 180 ° = 0 . M m P ' X P P P X M M " Y ' If m ...
Página 17
... equal ; so that PM = pm . Now PM represents by construction the sine of XOM , and pm the sine of XOm . Hence : The sines of supplementary angles are equal . In symbolic language this theorem is expressed thus : If a be any angle , then ...
... equal ; so that PM = pm . Now PM represents by construction the sine of XOM , and pm the sine of XOm . Hence : The sines of supplementary angles are equal . In symbolic language this theorem is expressed thus : If a be any angle , then ...
Otras ediciones - Ver todas
Elements of Plane and Spherical Trigonometry with Logarithmic and Other ... Simon Newcomb Sin vista previa disponible - 2016 |
Elements of Plane and Spherical Trigonometry: With Logarithmic and Other ... Simon Newcomb Sin vista previa disponible - 2018 |
Elements of Plane and Spherical Trigonometry: With Logarithmic and Other ... Simon Newcomb Sin vista previa disponible - 2017 |
Términos y frases comunes
9 Prop algebraic sign angle AOB angle corresponding angle XOM applied arithmetical complement circle circumference co-log co-ordinates coefficients column computation cos² cos³ cosec cosine cotangent Cotg differences distance divided Entering the table equal equations error example EXERCISES expression find log find the values formula fourth quadrant geometry gives greater Hence interpolation intersect latitude length line OX log cot measure metres minutes nth roots perpendicular places of decimals polar triangle polygon preceding problem projection quantities radius revolving right angle right triangle roots of unity secant sides sin a cos sin a sin sin² sine N sines and cosines spherical triangle spherical trigonometry square substituting subtract suppose Tang theorem third quadrant tions trigono trigonometric functions trihedral angle unit write wwww zero ΙΟ
Pasajes populares
Página 4 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 4 - The logarithm of a product is equal to the sum of the logarithms of its factors.
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 70 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Página 34 - To find the trigonometric functions corresponding to an angle between 45° and 90°, we take the degrees at the bottom of the page and the minutes in the right-hand column. The values of the...
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 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 53 - Conventionally the period is divided into 24 hours, each hour into 60 minutes, and each minute into 60 seconds.