A Treatise on Higher TrigonometryMacmillan, 1884 - 208 σελίδες |
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... sine and cosine is an innovation which seems fully justified by their im- portance in other subjects , and by the simplification effected by their use in the statement of many theorems and formulæ . I wish to thank the Master of ...
... sine and cosine is an innovation which seems fully justified by their im- portance in other subjects , and by the simplification effected by their use in the statement of many theorems and formulæ . I wish to thank the Master of ...
Σελίδα 23
... the expansion of cos ne is n ( -1 ) sin " 0 . ( 6 ) When n is odd the last term in the expansion of cos ne is n - 1 ( -1 ) 2 n cose.sin " -10 . EXPONENTIAL VALUES OF SINE AND COSINE . 21. By De RESULTS OF DE MOIVRE'S THEOREM . 23.
... the expansion of cos ne is n ( -1 ) sin " 0 . ( 6 ) When n is odd the last term in the expansion of cos ne is n - 1 ( -1 ) 2 n cose.sin " -10 . EXPONENTIAL VALUES OF SINE AND COSINE . 21. By De RESULTS OF DE MOIVRE'S THEOREM . 23.
Σελίδα 24
John Bascombe Lock. EXPONENTIAL VALUES OF SINE AND COSINE . 21. By De Moivre's Theorem , when n is any commen- surable number , and x any angle , ( cos nx + i sin nx ) is a value of ( cos x + i sin x ) ” . For x put the unit of angular ...
John Bascombe Lock. EXPONENTIAL VALUES OF SINE AND COSINE . 21. By De Moivre's Theorem , when n is any commen- surable number , and x any angle , ( cos nx + i sin nx ) is a value of ( cos x + i sin x ) ” . For x put the unit of angular ...
Σελίδα 25
... sine respectively , when the angle is expressed in circular measure . These results may be applied to prove any general formula in Elementary Trigonometry . EXAMPLE . Prove sin 2a 1+ cos 2a - tan a . 2i sin 2a e2ia - e - Qia = 2 + 2 cos ...
... sine respectively , when the angle is expressed in circular measure . These results may be applied to prove any general formula in Elementary Trigonometry . EXAMPLE . Prove sin 2a 1+ cos 2a - tan a . 2i sin 2a e2ia - e - Qia = 2 + 2 cos ...
Σελίδα 36
... sine be defined by the equations 2 cos 0 = a + ao , 2i sin 0 = ao - ď α then sin and cos satisfy the fundamental conditions " cos20 + sin20 = 1 , cos = = cos ( -0 ) , sin = − sin ( − 0 ) . - - ( 2 ) Prove that if a degree is the unit ...
... sine be defined by the equations 2 cos 0 = a + ao , 2i sin 0 = ao - ď α then sin and cos satisfy the fundamental conditions " cos20 + sin20 = 1 , cos = = cos ( -0 ) , sin = − sin ( − 0 ) . - - ( 2 ) Prove that if a degree is the unit ...
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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