Trigonometry ...1866 |
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Σελίδα 8
... tan A = OM ' OP secA = OM ' versA = 1 - cosA , OM cos A = OP ' OM cotA = = PM ' ОР cosecД = PM ' covers A1 - sinA . cos A means ( cos A ) 2 or the square of cosA , and so in similar cases . In the above figures A denotes any of the ...
... tan A = OM ' OP secA = OM ' versA = 1 - cosA , OM cos A = OP ' OM cotA = = PM ' ОР cosecД = PM ' covers A1 - sinA . cos A means ( cos A ) 2 or the square of cosA , and so in similar cases . In the above figures A denotes any of the ...
Σελίδα 9
... tan A ' sin A PM = cos A OP ÷ OP OP OM OM PM = = tanA , cos A 1 = = cotA . sinA tan A From the right - angled triangle POM we have OM2 PM2 OP2 cos2A + sin'A = + OP2 OP2 = = OP2 1 , sec2A = = OM2 cosec2 A OP2 OM2 + PM2 = OP2 PM2 = OM2 ...
... tan A ' sin A PM = cos A OP ÷ OP OP OM OM PM = = tanA , cos A 1 = = cotA . sinA tan A From the right - angled triangle POM we have OM2 PM2 OP2 cos2A + sin'A = + OP2 OP2 = = OP2 1 , sec2A = = OM2 cosec2 A OP2 OM2 + PM2 = OP2 PM2 = OM2 ...
Σελίδα 10
... is situated in the three other quadrants . Hence also tan ( -A ) sin ( -A ) - sinA cos ( -A ) COSA = tan A , .. cot ( -A ) == cotA , sec ( -A ) = 1 = 1 cos ( 4 ) cos A = = secA , cosec ( -A ) = 1 = 1 sin ( 10 [ 12 . PLANE TRIGONOMETRY .
... is situated in the three other quadrants . Hence also tan ( -A ) sin ( -A ) - sinA cos ( -A ) COSA = tan A , .. cot ( -A ) == cotA , sec ( -A ) = 1 = 1 cos ( 4 ) cos A = = secA , cosec ( -A ) = 1 = 1 sin ( 10 [ 12 . PLANE TRIGONOMETRY .
Σελίδα 11
... -4 ) = - cotA . COR . Hence tan ( 180 ° - A ) = sec ( 180 ° - A ) = cosec ( 180 ° - A ) = 1 cos ( 180 ° - A ) = 1 1 secA , - cos A = = cosecД . = 1 sin ( 180 ° - A ) ̄ ̄ sinĀ 14 . To prove that sin ( 180 ° + 13. ] PLANE TRIGONOMETRY . 11.
... -4 ) = - cotA . COR . Hence tan ( 180 ° - A ) = sec ( 180 ° - A ) = cosec ( 180 ° - A ) = 1 cos ( 180 ° - A ) = 1 1 secA , - cos A = = cosecД . = 1 sin ( 180 ° - A ) ̄ ̄ sinĀ 14 . To prove that sin ( 180 ° + 13. ] PLANE TRIGONOMETRY . 11.
Σελίδα 12
... tan ( 180 ° + A ) = = tanA , = tan A , cos ( 180 + A ) -cos .. cot ( 180 ° + 4 ) = cotA . 1 1 sec ( 180 ° + 4 ) = = cos ( 180 ° + 4 ) - secA , cos A 1 1 cosec ( 180 ° + A ) = = == cosecД . sin ( 180 ° + A ) sinA 15 . To prove that sin ...
... tan ( 180 ° + A ) = = tanA , = tan A , cos ( 180 + A ) -cos .. cot ( 180 ° + 4 ) = cotA . 1 1 sec ( 180 ° + 4 ) = = cos ( 180 ° + 4 ) - secA , cos A 1 1 cosec ( 180 ° + A ) = = == cosecД . sin ( 180 ° + A ) sinA 15 . To prove that sin ...
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angle POX increases angles terminated Cambridge centre circular measure coincides Conic Sections cos(a cos² cos4 cosB cosB+ cosec cosine cotA cotangent D.D. Dean D.D. Third Edition Dean of Ely decreases numerically Euclid EXAMPLES ON CHAPTER F. A. PALEY Fcap Fellow of St Fellow of Trinity Geometrical given angle given ratio Greek Hence J. R. SEELEY J. W. DONALDSON JONATHAN PALMER Late Fellow less than 90 log(s loga logarithms M.A. Fellow Mathematics negative and decreases P'OM Pembroke College perpendicular positive angle prove r₁ radius recensuit right-angled triangles POM secA secant Second Edition sides sin²A sin³A sinA sinB sine sine and cosine solution solve the triangle St John's College Students subtended subtract tanA tangent triangle ABC TRIGONO Trigonometrical Ratios Trinity College University of Cambridge values W. H. BESANT ОР
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