A Treatise on Higher TrigonometryMacmillan, 1884 - 208 σελίδες |
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Σελίδα 3
... true provided both these series are convergent . They are convergent for all values of n greater than 1 . Therefore they are arithmetically intelligible and true however great n may be . And in the limit , when n is in- finitely ...
... true provided both these series are convergent . They are convergent for all values of n greater than 1 . Therefore they are arithmetically intelligible and true however great n may be . And in the limit , when n is in- finitely ...
Σελίδα 8
... true for all values of r may be proved by induction , thus : Assume that the above expression ac = + R , where R is a quantity whose limit is zero when n is infinite ; multiply each side by the factor ( x ( x - 2 ) 41 хх n n 1 r + 1 ' 2 ...
... true for all values of r may be proved by induction , thus : Assume that the above expression ac = + R , where R is a quantity whose limit is zero when n is infinite ; multiply each side by the factor ( x ( x - 2 ) 41 хх n n 1 r + 1 ' 2 ...
Σελίδα 12
... true when A = a and B = b . - We shall often use the letter i as an abbreviation for √ - 1 . 12. De Moivre's Theorem . Whatever be the value of n positive or negative , integral or fractional , cos na + √ - 1 sin na is one of the ...
... true when A = a and B = b . - We shall often use the letter i as an abbreviation for √ - 1 . 12. De Moivre's Theorem . Whatever be the value of n positive or negative , integral or fractional , cos na + √ - 1 sin na is one of the ...
Σελίδα 13
... true . II . When n is a negative integer . Let n = - m . Then m is a positive integer . And ( cos a + √− 1 sin a ) ... true when n is a negative integer . III . When n is a fraction , positive or DE MOIVRE'S THEOREM . 13.
... true . II . When n is a negative integer . Let n = - m . Then m is a positive integer . And ( cos a + √− 1 sin a ) ... true when n is a negative integer . III . When n is a fraction , positive or DE MOIVRE'S THEOREM . 13.
Σελίδα 19
... true of ROP2 , ROP and of ROP , ROP , and so on . Hence n - 3 , 2π n x - cos √1 sin 2-2 , 2π and x - cos +1 sin 2π 2π n n n are factors of x - 1 . Their product is ( x - Cos 21 ) 2 + x- COS n + sin2 2π 2π 9 i.e. x2-2x cos +1 . n n ...
... true of ROP2 , ROP and of ROP , ROP , and so on . Hence n - 3 , 2π n x - cos √1 sin 2-2 , 2π and x - cos +1 sin 2π 2π n n n are factors of x - 1 . Their product is ( x - Cos 21 ) 2 + x- COS n + sin2 2π 2π 9 i.e. x2-2x cos +1 . n n ...
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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