Uniplanar Algebra: Being Part I of a Propædeutic to the Higher Mathematical AnalysisBerkeley Press, 1893 - 141페이지 |
도서 본문에서
ix 페이지
... ( sinh u ) | u = 1 , when u ___ 53. Area of a hyperbolic sector 55. Approximate value of natural base . . 54. Agenda : The addition theorem for hyperbolic ratios . 56. Agenda : Logarithmic forms of inverse hyperbolic ratios 65 55555558885 ...
... ( sinh u ) | u = 1 , when u ___ 53. Area of a hyperbolic sector 55. Approximate value of natural base . . 54. Agenda : The addition theorem for hyperbolic ratios . 56. Agenda : Logarithmic forms of inverse hyperbolic ratios 65 55555558885 ...
55 페이지
... sinh o = 0 , ― cosh o = 1 . ( 2 ) . cosh2 u sinh u = I. ( 3 ) . sech u + tanhu = I . ( 4 ) . coth2 u csch2 u = 1 . ( 5 ) . sinh 2 u = 2 sinh a cosh a . - ( 6 ) . cosh 2 u = : cosh ? u – sinh v ( 7 ) . cosh 2 u + 1 = 2 cosh2 u . ( 8 ) ...
... sinh o = 0 , ― cosh o = 1 . ( 2 ) . cosh2 u sinh u = I. ( 3 ) . sech u + tanhu = I . ( 4 ) . coth2 u csch2 u = 1 . ( 5 ) . sinh 2 u = 2 sinh a cosh a . - ( 6 ) . cosh 2 u = : cosh ? u – sinh v ( 7 ) . cosh 2 u + 1 = 2 cosh2 u . ( 8 ) ...
56 페이지
... to the right hand branch of the hyperbola its range of values is likewise between 1 and + ∞ ; hence we may assume 818 a - cosh u , and by virtue of the relations cosh2 u - sinh 56 GONIOMETRIC AND HYPERBOLIC RATIOS .
... to the right hand branch of the hyperbola its range of values is likewise between 1 and + ∞ ; hence we may assume 818 a - cosh u , and by virtue of the relations cosh2 u - sinh 56 GONIOMETRIC AND HYPERBOLIC RATIOS .
57 페이지
... sinh u = I , and - x2 | a2 — y2 | a2 = 1 , y sinh u . Also , since x2 a = - - y2 = a2 and x2 NQa2 , therefore NQ = NP , and we have x seccosh u , У = a a = tan 6 = sinh u , and the co - ordinates of Q being a , ß , also AH B α a sin ...
... sinh u = I , and - x2 | a2 — y2 | a2 = 1 , y sinh u . Also , since x2 a = - - y2 = a2 and x2 NQa2 , therefore NQ = NP , and we have x seccosh u , У = a a = tan 6 = sinh u , and the co - ordinates of Q being a , ß , also AH B α a sin ...
58 페이지
... sinh u ( Art . 48 ) it is called the Gudermannian of u * and is written gd u . Sin 0 , cos and tan 0 are then regarded as functions of u and are written sg u , cg u and tg u . 51. Agenda . From the definitions of the Guder- mannian ...
... sinh u ( Art . 48 ) it is called the Gudermannian of u * and is written gd u . Sin 0 , cos and tan 0 are then regarded as functions of u and are written sg u , cg u and tg u . 51. Agenda . From the definitions of the Guder- mannian ...
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a+ib addition and subtraction Addition Theorem affix Agenda amplitude angle AOQ arc AVQ arc-ratio assumed base CALIFORNIA circular sector co-ordinates commutative law complex quantities corresponding cosh COSK csch defined definition direction distance equal equation equilateral hyperbola expm exponential expressed factors formula functions geometric addition Goniometric Ratios Hence hyperbolic functions Hyperbolic Ratios hyperbolic sector imaginary indeterminate form integer inverse law of indices law of involution law of metathesis length logarithmic spiral logm metathesis modular normal modulus natural logarithms negative nth roots orthomorphosis parallel path plane polynomial positive Prop proportion PROPOSITION Prove the following quotient radius real axis real magnitudes real quantities reciprocal represent respectively roots sech sector sinh speed straight line tanh tensor tion triangle unit circle x+iy z-plane zero