D Properties and Measurement
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1 APPENDIX D. Review of Alge, Geomet, nd Tigonomet A D Popetie nd Meuement D. Review of Alge, Geomet, nd Tigonomet Alge Popetie of Logitm Geomet Plne Anltic Geomet Solid Anltic Geomet Tigonomet Li of Function Alge Opetion wit Eponent. n m nm.. m nm 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... n fcto 0, 0. n 0 *., n n n 5. n n 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.
2 A APPENDIX D Popetie nd Meuement.. c d c c d cd d d c c c c c 5. c c c d c d c d Qudtic Fomul c 0 ± c Fcto nd Specil Poduct.... Fctoing Gouping c d c d c d c d c d Binomil Teoem n n n n... n n n nn! n nn n! n
3 APPENDIX D. Review of Alge, Geomet, nd Tigonomet A 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.. Fctoil: 0!,!,!,!,!, etc. Sequence. Aitmetic:. Geometic:,,,,, 5,... 0,,,,, 5, n n. Genel monic:. Hmonic: 5. p-sequence: Seie,,,,, 5,...,,,, 5,... p, p, p, p, 5 p, n n..., 5... n n..., ln e!! 5! 5!... n n!..., < <... n n n < <..., 0 < < 0 < in 5 7! 5! 7!..., < <
4 A APPENDIX D Popetie nd Meuement 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.
5 APPENDIX D. Review of Alge, Geomet, nd Tigonomet A5 Geomet (Continued). Equiltel tingle Heigt Ae Iocele igt tingle Ae 5 5 Qudiltel (Fou-Sided Figue). Rectngle. Sque Ae lengtwidt lw Ae ide w. Pllelogm. Tpezoid Ae Ae
6 A6 APPENDIX D Popetie nd Meuement 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
7 APPENDIX D. Review of Alge, Geomet, nd Tigonomet A7 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: A B C 0 Hoizontl line:
8 A8 APPENDIX D Popetie nd Meuement 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 Vete Ai Focu Diecti p < 0 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
9 APPENDIX D. Review of Alge, Geomet, nd Tigonomet A9 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,, z z Eqution of Spee Cente:, k, l, Rdiu: k z l Tigonomet 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
10 A0 APPENDIX D Popetie nd Meuement 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
11 APPENDIX D. Review of Alge, Geomet, nd Tigonomet A 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 in co in in co in in in
12 A APPENDIX D Popetie nd Meuement Li of Function Algeic Function Line o Fit-Degee Qudtic o Second-Degee Cuic o Tid-Degee Polnomil Polnomil Polnomil f 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
13 APPENDIX D. Review of Alge, Geomet, nd Tigonomet A Li of Function (Continued) Eponentil nd Logitmic Function Eponentil Function Eponentil Function Logitmic Function f, > f, 0 < < f ln Tigonometic Function π π π π π π π π Sine Function Coine Function Tngent Function f in f co f tn π π π π π π π π Coecnt Function Secnt Function Cotngent Function f cc f ec f cot Nonelement Function Aolute Vlue Function Compound Function Step Function f f,, < f
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