MhScop g of 9 FORMULAE SHEET If h lik blow r o-fucioig ihr Sv hi fil o your hrd driv (o h rm lf of h br bov hi pg for viwig off li or ju coll dow h pg. [] Trigoomry formul. [] Tbl of uful rigoomric vlu. [3] Hyprbolic fucio. [4] Tbl of drd diffril. [5] Wlli formul [6] Tbl of drd igrl [7] Ivr rigoomricl d hyprbolic fucio. [8] iomil pio formul [9] Lplc Trform [] Idii: i A co A Trigoomric Formul c A A coc A co A [] Formul for h ddiio d ubrcio of gl: i A = i Aco co Ai i A = i Aco co Ai co A = co Aco i Ai co A = co Aco i Ai From h dfiiio of h g w c u h l of formul o giv: A = A A = A ( A ( A
MhScop g of 9 i Aco = ( i ( A i ( A co Ai = ( i ( A i ( A co Aco = co A co A i Ai = co A A ( co [3] y ddig or ubrcig h formul i cio [] w obi h formul:- [3b] From h bov w c driv h followig:- A A A A i A i = i co i A i = co i A A A A co A co = co co co A co = i i [4] Drivd idi coa coa co A= i A= i A= i Aco A co = co i A A A = A co = i A [5] A uful ubiuio ud i igrio: A If =, i A=, co A=, A= Tbl of Uful Vlu i co rd 3 6 rd 45 4 rd 6 3 rd 3 3 3 3 9 rd 8 rd -
MhScop g 3 of 9 Hyprbolic Fucio ic dfiiio: ih = coh = ih h = = = = coh Idii: coh ih = ch = h coch = coh Formul: ih = ih coh coh coh ih coh = = coh = ih coh coh = ih = For mor iv li of hyprbolic formul click hr (o rur o hi po fr viwig h docum u h ck uo Tbl of Sdrd Diffril Coffici ' f ( f ( f ( f ' l ( > l ( > i co ih coh co i coh ih c h ch coc coc co coch coch coh c c ch ch h co coc coh coch i ( < < ih 3
MhScop g 4 of 9 co < < ( coh h ( > ( < < Wlli Formul ( ( ( ( ( ( ( ( 3...4. i d= co d= = 3,5,7,9... 4...5.3 3...3. 4...4. =, 4,6,8... ( 3...( 3 ( m ( m... m m m i co d= A A = if m d r boh v poiiv igr A = if m d/or r odd poiiv igr. Tbl of Sdrd Igrl f ( f d f ( f i l ( l co ih coh d ( > co i coh ih c h l coh coc l coch l h 4
MhScop g 5 of 9 c l c ch co l i coh l ih i i 4 co i 4 > ( i < < 4 coh ih 4 h < < coh > > ih ( > ih ih ( > > coh Ivr Fucio [] Ivr Trigoomric fucio. ( y = i i h gl who i i. No: i i mulivlud fucio. Th pricipl vlu of i (or rci i h umbr lyig i h irvl which ifi h quio i =,. (b y = co i h gl who coi i. No: co i mulivlud fucio. Th pricipl vlu of co (or rcco i h umbr lyig i h irvl which ifi h quio co =,. (c y = i h gl who g i. No: i mulivlud fucio. Th pricipl vlu of (or rc i h umbr lyig i h irvl which ifi h quio =,. ALL oluio of h quio i y = r giv by y = ( Whr hr 5 i =, i. = i (from your clculor y, d my b y igr ALL oluio of h quio co y = r giv by y = ±. Whr hr co =, d my b y igr
MhScop g 6 of 9 ALL oluio of h quio y = r giv by y = Whr hr =, d my b y igr [] Ivr Hyprbolic fucio. ih i h umbr y which ifi h quio ih y =. coh i h umbr y lyig i h irvl y which ifi h quio coh y =,. h coh i h umbr y which ifi h quio h y =, <. i h umbr y which ifi h quio coh y =, > W c pr h hyprbolic ivr fucio i rm of fucio of h url logrihm ih = l coh = l h = l < coh = l > Th iomil Coffici 3 ( = c c c 3 (...( r... Whr c r = r! Th rul i vlid for ll if i poiiv igr d for < for ll ohr vlu of. Th grl biomil pio Suppo w r rquird o pd ( b W um h h rm d b (wih irchg of ymbol if cry r uch h > b Th w c wri: b b ( b Hr < Th cod rm i h produc c b pdd uig h rul i h opig cio. 3 b ( = c c c 3... (Rplc by So w c wri: 6
MhScop g 7 of 9 r b b b b b = = c c... c r... rformig h muliplicio giv: ( ( ( 3 3 ( b = b b b...! 3! ( (...( ( r r r b... r! If i poiv igr h hi ri i fii d w hv: b b b b! 3! (...( ( r r r b... b r! 3 3 =... TALE OF LALACE TRANSFORMS f ( F k ( H (! k k! k k i co ( ( i ( k 7
MhScop g 8 of 9 k co( ih coh ( ( k k ( i ( co( ( ( 8
MhScop g 9 of 9 SOME RULES OF LALACE TRANSFORMS f (, g(, h( F, G, H f ( f( d f ( bg( k f F( bg( ( F ( k (Liriy (Shif i f ( F( f ( f ( Ff f ( ( ( f ( ( F f f f f ( u du H( f ( f ( T = f ( f( g d F ( ( ( ( F f ( d d F ( ( (Shif i T f( d T (riodic fucio F G (Covoluio f ( d F d f( Fudu { F } lim f( = lim lim f( = lim { F } 9