A Treatise on Higher TrigonometryMacmillan, 1884 - 208 σελίδες |
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Σελίδα 44
... cosh x stands for e * + ex 2 and sinh x for e * - 2 cosh x and sinh x are abbreviations respectively for the words hyperbolic cosine of x and hyperbolic sine of x . We shall use the notation coshx for ( cosh x ) , etc. EXAMPLES . XX ...
... cosh x stands for e * + ex 2 and sinh x for e * - 2 cosh x and sinh x are abbreviations respectively for the words hyperbolic cosine of x and hyperbolic sine of x . We shall use the notation coshx for ( cosh x ) , etc. EXAMPLES . XX ...
Σελίδα 45
... cosh nx . 2 cosh x = 2 cosh ( n + 1 ) x + 2 cosh ( n − 1 ) x . II . = 1 , and we obtain In I. put n = - 2o cos2 a = 2 cos 2a + 2 . Multiply each side of the result by 2 cos a , then 23 cos3 a = 2 cos 2a . 2 cos a + 4 cos a . But by I ...
... cosh nx . 2 cosh x = 2 cosh ( n + 1 ) x + 2 cosh ( n − 1 ) x . II . = 1 , and we obtain In I. put n = - 2o cos2 a = 2 cos 2a + 2 . Multiply each side of the result by 2 cos a , then 23 cos3 a = 2 cos 2a . 2 cos a + 4 cos a . But by I ...
Σελίδα 46
... cosh x , and in this term the factor 2 is to be omitted . n - 1 2 * 49 . To prove , when n is odd , that ( −1 ) 2a sin " a can be expressed in terms of sin na , sin ( n - 2 ) a , etc .; that 2 " sinh nx can be expressed in terms of ...
... cosh x , and in this term the factor 2 is to be omitted . n - 1 2 * 49 . To prove , when n is odd , that ( −1 ) 2a sin " a can be expressed in terms of sin na , sin ( n - 2 ) a , etc .; that 2 " sinh nx can be expressed in terms of ...
Σελίδα 47
... cosh n . 2 sinh x = 2 cosh ( n + 2 ) x 4 cosh nx + 2 cosh ( n − 2 ) x . - - Following the argument of the last article , we have since ( − 1 ) 22 sin2 a = 2 cos 2a - 2 , and 2o sinh3 x = 2 cosh 2x - 2 . And since 2 " sinh ” x = ( e ...
... cosh n . 2 sinh x = 2 cosh ( n + 2 ) x 4 cosh nx + 2 cosh ( n − 2 ) x . - - Following the argument of the last article , we have since ( − 1 ) 22 sin2 a = 2 cos 2a - 2 , and 2o sinh3 x = 2 cosh 2x - 2 . And since 2 " sinh ” x = ( e ...
Σελίδα 48
... cosh nx can be ex- pressed in powers of cosh x ; and that the two expressions are the same in form . We have , when n is a positive integer 2 cos ( n + 1 ) a = 4 cos na . cos a - 2 cos ( n − 1 ) a . - ( I. ) 2 cosh ( n + 1 ) x = 4 cosh ...
... cosh nx can be ex- pressed in powers of cosh x ; and that the two expressions are the same in form . We have , when n is a positive integer 2 cos ( n + 1 ) a = 4 cos na . cos a - 2 cos ( n − 1 ) a . - ( I. ) 2 cosh ( n + 1 ) x = 4 cosh ...
Άλλες εκδόσεις - Προβολή όλων
TREATISE ON HIGHER TRIGONOMETR J. B. (John Bascombe) 1849-1921 Lock Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
a+ẞ Algebra angular points arithmetical ascending powers calculated Cambridge centre circular measure circumscribing circle Classical Series coefficients cos² cos³ cosec cosh nx cosine Crown 8vo deduce different values distance Edited by Rev equal escribed circles Eton College EXAMPLES Expand expression Extra fcap fcap Fellow of St Find form A+iB formula GRAMMAR greater Hence inscribed inscribed circle integer Introductions and Notes J. P. MAHAFFY John's College King's College late Fellow less limit LIVY logarithms MACMILLAN'S CLASSICAL CATALOGUE Moivre's Theorem nine-points circle nth roots obtain Oxford P₁ perpendiculars positive integer Prove the following quadratic factors radii radius right angle roots School sec² Shew sides sin n sin² sin³ sine sinh Sum the series Tables tan-¹ tan² tangent triangle ABC Trigonometry Trinity College Vocabulary whole number
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