This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1865 Excerpt: ...A sin B = cos (A--B); therefore by addition, 2 cosi cos.8 = cos (A + B)+ cos (A--B) (3); and by subtraction, --2sin.4 sin B = cos (A+B)--cos (A--B) ).... or 2sin4 sinjB = cos(--B)--Cob(a+b) j W" It will be found well worth while to learn these H formulae as given above, and also expressed verbally as follows: --Of any ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1865 Excerpt: ...A sin B = cos (A--B); therefore by addition, 2 cosi cos.8 = cos (A + B)+ cos (A--B) (3); and by subtraction, --2sin.4 sin B = cos (A+B)--cos (A--B) ).... or 2sin4 sinjB = cos(--B)--Cob(a+b) j W" It will be found well worth while to learn these H formulae as given above, and also expressed verbally as follows: --Of any two angles, 2 sin one. cos the other = sin sMm+sin difference... (1). 2 cos one. sin the other = sin' sum--sin difference... (2). 2 cos one. cos iAe other = cos sum+cos difference... (3).--2 sin owe. sin the other = cos sum--cos difference' or 2 sin owe. sin (lie other = cos difference--cos sum.. 83. As before seen, sin(+5) + sin(--J5) = 2 sin cos B. A + B Since bere A and 5 may have any values, put-----A Jj for A and-----for B. We shall then require to replace A + B by A, for A + B 4-5.-2+"-; and A--BbjB, for + 5-J9_ B A and B are any angles; and we may therefore say: Of any two angles, sin one + sin the other = 2 sin semi-sum. cos semi-difference...(5). sin owe--sin the other = 2 cos semi-sum. sin semi-difference... (6). cos o/te + cos tte otter = 2 cos semi-sum. cos semi-difference..(7). cos owe--cos tte otter =--2amsemi-sum. aiasemi-differenee...(8). Exercise VI.--(1.) Given formulae (1) and (2) above, verify that sin A cos B + cos A sin B = sin (4 + B). sin 4 cos B + cos 4 sin B--2 sin A cos B + 2 cos A sin B 2 = sin (4 + B)+sin (4-B)+sin (4 + B)-sin (A-B) and sin----cos-= /!--sin.4... (10); adding (10) to (9), and subtracting (10) from (9), we obtain A 2 sin = il + sml, /l--sin 4...(11); j and 2 cos g = -/T+smA 1--sin A... (12). When the value of A, or the quadrant to which it belongs, is given, formulae (11) and (12) may be obtained with single instead of double signs. This is done by first determining the pro...
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