A Treatise on Higher TrigonometryMacmillan, 1884 - 208 σελίδες |
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Σελίδα 35
... divided into n equal arcs PP , PP , ... P - 1 Po . Hence , whatever be the integral is represented by one of the value of r , the angle + angles ROP , ROP ,, etc. 21π n Hence in general there are n different values and no more of cos ...
... divided into n equal arcs PP , PP , ... P - 1 Po . Hence , whatever be the integral is represented by one of the value of r , the angle + angles ROP , ROP ,, etc. 21π n Hence in general there are n different values and no more of cos ...
Σελίδα 43
... divided by three , is equal to the length of the arc , nearly . ( 12 ) Prove by induction n tan - n ( n − 1 ) ( n - 2 ) 1.2.3 tan3 0+ . tan no = n ( n - 1 ) 1 tan20 + ...... 1.2 h2 13 ( 13 ) sin ( 0 + h ) = sin 0 + h cos 0 . sin 0- cos ...
... divided by three , is equal to the length of the arc , nearly . ( 12 ) Prove by induction n tan - n ( n − 1 ) ( n - 2 ) 1.2.3 tan3 0+ . tan no = n ( n - 1 ) 1 tan20 + ...... 1.2 h2 13 ( 13 ) sin ( 0 + h ) = sin 0 + h cos 0 . sin 0- cos ...
Σελίδα 63
... divided by the sine of half the difference . EXAMPLE 3. To prove that if np = 2π , then sin a + sin ( a + 4 ) + sin ( a + 24 ) for all values of a . ... + sin { a + ( n - 1 ) ø } = 0 In the result of Example 1 , sin and occurs in the ...
... divided by the sine of half the difference . EXAMPLE 3. To prove that if np = 2π , then sin a + sin ( a + 4 ) + sin ( a + 24 ) for all values of a . ... + sin { a + ( n - 1 ) ø } = 0 In the result of Example 1 , sin and occurs in the ...
Σελίδα 112
... divided respectively by sin A , sin B , sin C. ( 7 ) It is observed that the altitude of the top of a moun- tain at each of the points AB and C where ABC is a horizontal triangle is a . Shew that the height of the mountain is a tan a ...
... divided respectively by sin A , sin B , sin C. ( 7 ) It is observed that the altitude of the top of a moun- tain at each of the points AB and C where ABC is a horizontal triangle is a . Shew that the height of the mountain is a tan a ...
Σελίδα 121
... divided by CB , BA into three parts which are in the ratio sin2 : 2sin . sin1⁄2B . sinС : sin2C . ( 26 ) If a point be taken in an equilateral triangle such that its distances from the angular points are proportional to the sides of a ...
... divided by CB , BA into three parts which are in the ratio sin2 : 2sin . sin1⁄2B . sinС : sin2C . ( 26 ) If a point be taken in an equilateral triangle such that its distances from the angular points are proportional to the sides of a ...
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angle Assistant-Master BOOKS calculated Cambridge centre CHAPTER circle circumscribing Classical coefficients cos² cos³ cosec cosh cosine Crown 8vo deduce difference distance divided Edited equal equation error escribed EXAMPLES expansion expression factors fcap Fellow Find formula given giving GRAMMAR greater Greek height Hence identity importance inscribed circle Introduction late Fellow LATIN length less limit logarithms magnitude measure method Multiply nearly Notes observed obtain Oxford points positive integer powers preparation Professor PROSE Prove quantity radii radius ratio Ready respectively result revised right angle roots Rule School Shew sides sin n sin² sin³ sine sinh Solve stands Tables tangent theorem Translated triangle triangle ABC Trigonometry Trinity College true University Vocabulary write
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