Uniplanar Algebra: Being Part I of a Propædeutic to the Higher Mathematical AnalysisBerkeley Press, 1893 - 141페이지 |
도서 본문에서
11개의 결과 중 1 - 5개
55 페이지
... cosh , tanh , coth , sech , csch , are defined by the following identities : sinh u = } ( * = † ( eu — e − u ) ... cosh o = 1 . ( 2 ) . cosh2 u sinh u = I. ( 3 ) . sech u + tanhu = I . ( 4 ) . coth2 u csch2 u = - I. ( 5 ) . sinh 2 a = 2 ...
... cosh , tanh , coth , sech , csch , are defined by the following identities : sinh u = } ( * = † ( eu — e − u ) ... cosh o = 1 . ( 2 ) . cosh2 u sinh u = I. ( 3 ) . sech u + tanhu = I . ( 4 ) . coth2 u csch2 u = - I. ( 5 ) . sinh 2 a = 2 ...
56 페이지
... cosh u has I for its smallest and ∞ for its largest value corresponding to u = o and ∞ respectively , and if the variations of x / a be confined to the right hand branch of the hyperbola its range of values is likewise between 1 and + ...
... cosh u has I for its smallest and ∞ for its largest value corresponding to u = o and ∞ respectively , and if the variations of x / a be confined to the right hand branch of the hyperbola its range of values is likewise between 1 and + ...
57 페이지
... cosh u , y = = tan 6 : sinh u , α α and the co - ordinates of Q being a , ß , also АН В y α a = sin tanh “ , cos = sech u , a a x a x and finally , since OBK is similar to ONP and a2 = y • LO , * a BK x У LO a coth u , = csch u . α y ...
... cosh u , y = = tan 6 : sinh u , α α and the co - ordinates of Q being a , ß , also АН В y α a = sin tanh “ , cos = sech u , a a x a x and finally , since OBK is similar to ONP and a2 = y • LO , * a BK x У LO a coth u , = csch u . α y ...
62 페이지
... cosh u and y│a = = x + 2 2 ; a ; = sinh u , pn eu . n a2 Area of OAP , .. P = ( eu In - e - u 4 a u sinh ( u | nh 2 ... cosh + cosh a sinh v ( 2 ) . cosh ( u + v ) = cosha cosh a – sinh “ sinh . ( 3 ) . tanh ( u + v ) = tanh u + tanh v ...
... cosh u and y│a = = x + 2 2 ; a ; = sinh u , pn eu . n a2 Area of OAP , .. P = ( eu In - e - u 4 a u sinh ( u | nh 2 ... cosh + cosh a sinh v ( 2 ) . cosh ( u + v ) = cosha cosh a – sinh “ sinh . ( 3 ) . tanh ( u + v ) = tanh u + tanh v ...
63 페이지
... cosh u the ratios NP / a and ON a . [ Burn- side : Messenger of Mathematics , vol . xx , pp . 145-148 . ] ( 5 ) . In the figure of Art . 53 show that the trapezoids SAPS , SP , P , S ,, etc. , are equal in area to the corre- sponding ...
... cosh u the ratios NP / a and ON a . [ Burn- side : Messenger of Mathematics , vol . xx , pp . 145-148 . ] ( 5 ) . In the figure of Art . 53 show that the trapezoids SAPS , SP , P , S ,, etc. , are equal in area to the corre- sponding ...
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addition and subtraction Addition Theorem Agenda amplitude angle AOQ arc-ratio B₁ base called circular sector cis ẞ commutative law complex quantities COROLLARY corresponding cosh COSK csch defined definition denoted distance equal equation equilateral hyperbola expm exponential expressed formula functions geometric addition Goniometric Ratios Hence hyperbolic functions Hyperbolic Ratios hyperbolic sector imaginary indeterminate form integers intersect inverse law of indices law of involution law of metathesis length logarithmic spiral logarithms logm modulus Multiplication and Division natural logarithms negative factors nth root OJ=j parallel plane polynomial positive Prop proportion PROPOSITION Prove the following quotient radii radius real axis real magnitudes real quantities reciprocal represent respectively sech sector sinh speed of Q straight line tanh tensor tion triangle unit circle z-plane zero