Appendi D: Fomul, Popetie nd Meuement Review of Alge, Geomet, nd Tigonomet Unit of Meuement D. REVIEW OF ALGEBRA, GEOMETRY, AND TRIGONOMETRY Alge Popetie of Logitm Geomet Plne Anltic Geomet Solid Anltic Geomet Tigonomet Li of Function Alge Opetion wit Eponent. n m nm. nm. m n n. 5. n m nm 6. n n 7. c n c n 8. nm nm n n n n n Eponent nd Rdicl (n nd m e poitive intege). n.... 0, 0 n fcto. n 0 *., n n n 5. n n 6. 7. mn n m n m mn m n n m Opetion wit Fction.. c d d d d c d c d c d d d c d d d d c d c d c d d d * If n i even, te pincipl nt oot i defined to e poitive.
.. 5. c d c c c c d c d cd d d c c c c c Qudtic Fomul c d c d c 0 ± c Fcto nd Specil Poduct.... Fctoing Gouping c d c d c d c d c d Binomil Teoem.... 5. 6. 7. 6 6 n n n n... n n n nn! n nn n! n
Alge (Continued) 8. n n n n... ± n n n nn! n nn n! n Micellneou. If 0, ten 0 o 0.. If c c nd c 0, ten. 0!,!,!,!,!,. Fctoil: etc. Sequence. Aitmetic:. Geometic:,,,,, 5,... 0,,,,, 5,... 0... n n. Genel monic:. Hmonic: 5. p-sequence:,,,,, 5,...,,,, 5,... p, p, p, p, 5 p,... Seie... n n..., 5... n n..., ln e!! 5! 5!... n n!..., in 5 7! 5! 7!...,... n n n..., 0 < < < < 0 < < < < <
co! 6! 6!..., k k k k kk! kk! kk k! kk k! kk k k! kk k k!...,..., < < < < * < < * Popetie of Logitm Invee Popetie. ln e. e ln Popetie of Logitm. ln 0.. ln ln ln. 5. ln ln 6. ln e ln ln ln log ln ln Geomet Tingle. Genel tingle Sum of tingle 80 Ae (e)(eigt) α β θ. Simil tingle A B β α A β B α. Rigt tingle c (Ptgoen Teoem) α c Sum of cute ngle 90 β * Te convegence t depend on te vlue of k. ±
Geomet (Continued). Equiltel tingle Heigt Ae 60 60 60 5. Iocele igt tingle Ae 5 5 Qudiltel (Fou-Sided Figue). Rectngle. Sque Ae lengtwidt lw Ae ide w. Pllelogm. Tpezoid Ae Ae
Cicle nd Ellipe. Cicle. Secto of cicle in din Ae Cicumfeence Ae θ. Cicul ing. Ellipe Ae R R Ae Cicumfeence Solid Figue. Cone A e of e Volume A A. Rigt cicul cone Volume Ltel ufce e. Futum of igt cicul cone Volume R R Ltel ufce e R R
Geomet (Continued). Rigt cicul clinde Volume Ltel ufce e 5. Spee Volume Sufce e Plne Anltic Geomet Ditnce Between, nd, d Midpoint Between, nd, Midpoint, Slope of Line Ping Toug, nd, m Slope of Pllel Line m m Slope of Pependicul Line m m Eqution of Line Point-lope fom: m Veticl line: Genel fom: Hoizontl line: A B C 0
Eqution of Cicle Cente:, k, Rdiu: Stndd fom: k Genel fom: A A D E F 0 Eqution of Pol Vete:, k Focu: (, k + p) Vete: (, k) Ai: = p > 0 Diecti: = k p Ai Diecti Vete p < 0 Focu Diecti: = p p > 0 Focu: ( + p, k) Vete: (, k) Ai: = k Diecti Vete Focu p < 0 Ai p k k p () Veticl i: p > 0 () Veticl i: p < 0 (c) Hoizontl i: p > 0 (d) Hoizontl i: p < 0 Eqution of Ellipe Cente:, k (, k) (, k) k k
Plne Anltic Geomet (Continued) Eqution of Hpeol Cente:, k (, k + c) ( c, k) (, k ) ( + c, k) (, k) (, k c) k k Solid Anltic Geomet Ditnce Between,, z nd,, z d z z Midpoint Between,, z nd,, z Midpoint Eqution of Plne A B Cz D 0 Eqution of Spee Cente:, k, l, Rdiu: k z l Tigonomet,, z z Definition of te Si Tigonometic Function Rigt tingle definition: 0 < < in opp. p. co dj. p. tn opp. dj. cc p. opp. ec p. dj. cot dj. opp. θ Hpotenue Adjcent Oppoite
Cicul function definition: i n ngle nd, i point on te teminl of te ngle. in cc (, ) = + co ec θ tn cot Sign of te Tigonometic Function Qudnt Qudnt in co tn cot ec cc I II III IV Tigonometic Identitie Recipocl identitie in cc cc in tn in co co ec ec co cot co in tn cot cot tn Ptgoen identitie in co Reduction fomul in in in in tn ec co co co co cot cc tn tn tn tn
Tigonomet (Continued) Sum o diffeence of two ngle in co tn ± in co ± co in ± co co in in ± tn ± tn tn tn in in in in co co co in Doule-ngle identitie in in co co co in tn tn tn Multiple-ngle identitie in in in co co co tn tn tn tn in in co 8 in co co 8 co 8 co tn tn tn 6 tn tn Hlf-ngle identitie in co co co Poduct identitie in in co co co co co co co in in in
Li of Function Algeic Function Line o Fit-Degee Polnomil Qudtic o Second-Degee Cuic o Tid-Degee Polnomil f Polnomil f f Fout-Degee Polnomil f Fift-Degee Polnomil f 5 6 Rtionl Function Rtionl Function Rtionl Function f f f 5 Sque Root Function f Cue Root Function f
Li of Function (Continued) Eponentil nd Logitmic Function Eponentil Function Eponentil Function Logitmic Function f, > f, 0 < < f ln Tigonometic Function Sine Function Coine Function Tngent Function f in f co f tn Coecnt Function Secnt Function Cotngent Function f cc f ec f cot Nonelement Function Aolute Vlue Function Compound Function Step Function f f f, <,