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Side 24
... cosB + cos A sinB . ON - MN ON- QR = = ОР ОР 9 ON OQ QR PQ OQ OP PQ OP ' cosД cosB- sinA sinB . * 28 . To find the tangent of A + ( 24 ) [ 27 .
... cosB + cos A sinB . ON - MN ON- QR = = ОР ОР 9 ON OQ QR PQ OQ OP PQ OP ' cosД cosB- sinA sinB . * 28 . To find the tangent of A + ( 24 ) [ 27 .
Side 26
... cosB + sin 4 sin B. - To find the tangent of A – B in terms of the tangents of A and B. ( See fig . Art . 29. ) PM RM- PR tan ( A - B ) = OM ON + MN ' QN - PR = ON + QR ' = QN PR ON ON QR 1+ ON QN PR ON ON 1+ QR QN ' QN ' ON Now from ...
... cosB + sin 4 sin B. - To find the tangent of A – B in terms of the tangents of A and B. ( See fig . Art . 29. ) PM RM- PR tan ( A - B ) = OM ON + MN ' QN - PR = ON + QR ' = QN PR ON ON QR 1+ ON QN PR ON ON 1+ QR QN ' QN ' ON Now from ...
Side 27
... QR perpendicular to PM . x M Then the angle QPR = 90 ° - PQR = RQO = A. PM RM + PR Now sin ( A + B ) : = OP OP QN + PR OP " QN OQ PR PQ = + OQ OP PQ'OP ' = sinA cosB + cos A sin B. -X N OM ON - MN cos ( A + B ) 31. ] 27 PLANE TRIGONOMETRY .
... QR perpendicular to PM . x M Then the angle QPR = 90 ° - PQR = RQO = A. PM RM + PR Now sin ( A + B ) : = OP OP QN + PR OP " QN OQ PR PQ = + OQ OP PQ'OP ' = sinA cosB + cos A sin B. -X N OM ON - MN cos ( A + B ) 31. ] 27 PLANE TRIGONOMETRY .
Side 28
... cos ( B– A ) . Now since B - A is positive and B and A each less than 90 ° , the formulae ( 3 ) and ( 4 ) hold for sin ( B - A ) and cos ( B — A ) . .. sin ( B - A ) = sinB cosA - cosB sinД , and cos ( B - A ) = cos B cosA + sinBsinA ...
... cos ( B– A ) . Now since B - A is positive and B and A each less than 90 ° , the formulae ( 3 ) and ( 4 ) hold for sin ( B - A ) and cos ( B — A ) . .. sin ( B - A ) = sinB cosA - cosB sinД , and cos ( B - A ) = cos B cosA + sinBsinA ...
Side 29
... cos B'- cosA ' sin B ' , by what has been already shewn . = -sin ( -A ) cos ( -B ) — cos ( -A ) sin ( — B ) , - = sinA cosB + cos sin B. Similarly the other formulae can be shewn to hold good when A and B are both negative , or when ...
... cos B'- cosA ' sin B ' , by what has been already shewn . = -sin ( -A ) cos ( -B ) — cos ( -A ) sin ( — B ) , - = sinA cosB + cos sin B. Similarly the other formulae can be shewn to hold good when A and B are both negative , or when ...
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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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