ALGEBRA 2/TRIGONMETRY TOPIC REVIEW QUARTER 3 LOGS
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1 ALGEBRA /TRIGONMETRY TOPIC REVIEW QUARTER LOGS Cnverting frm Epnentil frm t Lgrithmic frm: E B N Lg BN E Americn Ben t French Lg Ben-n Lg Prperties: Lg Prperties lg (y) lg + lg y lg y lg lg y lg () lg Epnentil Grwth: y b initil, b grwth rte (± %), time Cmpund Interest Frmul: A P( + n r ) nt A Amunt, P Principl, r rte, t time, n # times cmpunded, Cmpunded Cntinuusly Frmul: A Pe rt Chnge f Bse Frmul: b n lg n lg b A Amunt, P Principl, r rte, t time, e is cnstnt π ) Wht is 8 written in lgrithmic frm? () lg 8 π () lg 8 π () lg π 8 (4) π lg 8 ) In the digrm belw, figure b is the reflectin f y in the line y. Which is n epressin fr the equtin f figure b? () y () lg () y lg (4) y y ( ) ) Which f the fllwing is the inverse reltin f lg? y 4 () 4 y () 4 y () 4 y (4) y 4 4) (y) The epressin ln z is equivlent t () ln + lny ln z () (ln + lny) ln z () (ln + lny) ln z (4) (ln + ln y ln z) ) The epressin lg lgb is equivlent t () lg b () lg () b lg (4) lg( b ) b
2 SOLVING LOG EQUATIONS Prcedure fr Slving Lg Equtins: ) Use the lg prperties t simplify bth sides. ) Cse : If yu hve lg lg r ln ln, drp the lg frm bth sides nd slve fr the given vrible. Cse : If it s lg: Cnvert frm lg frm t epnentil frm nd then slve fr the given vrible. Cse : If it s ln: Use e t und it. ) Check yur nswers bck int the ORIGINAL equtin. Nte, yu cnnt tke the lg f negtive number r 0. Nturl Lgs: lgs with the bse f e ln lg e Slving Nturl Lg equtins: e. Given: ln 4, slve fr. Mke ech side n epnent f e: e ln e 4 The e nd ln cncel: e 4 Slving Bse e equtins: e. Given: e, slve fr. Mult ech side by the nturl Lg: ln e ln The e nd ln cncel: ln 6) Slve fr : lg ( ) + lg( + ) () 7, nly () {-7,} (), nly (4) {-, 7} 7) Slve fr t the nerest tenth: (.) 00 8) Slve the given equtin fr, t the nerest hundredth: e 7
3 TRIG (UNIT CIRCLE-RECIPORCAL FUNCTIONS-ARC LENGTH) Trignmetric Functins Oppsite Sin Hyptenuse Adjcent Cs Hyptenuse Oppsite Tn Adjcent OR Sin Cs Reciprcl Functins Csc Hyptenuse Oppsite Sec Hyptenuse Adjcent Adjcent Ct Oppsite OR Cs Sin 80 /-80 Qud II Sin psitive (-, 0) Qud III Tn psitive (0, ) 90 /-70 (0, -) 70 /-90 y Qud I All psitive (, y) (cs, sin ) (, 0) Qud IV Cs psitive Angles cn be mesured in degrees OR rdins. π Cnverting t rdins: Multiply by Cnverting t degrees: Multiply by π Finding Arc Length: Use the frmul: S r S rc length r rdius centrl ngle (MUST BE IN RADIANS!!) DMS: Cn be fund by pressing nd APPS Cfunctins: Tw trignmetric functins tht equl ech ther when the ngles dd up t 90. Emple: Sin Cs 7 Sec 8 Csc 9 Tn 40 Ct 0 Ect Vlues: Sin Cs 4 Sin Cs 0 Tn Tn Pythgren Identity: cs + sin cs cs sin + cs cs sin + sin sin cs sin + tn ct sec + csc 9) The terminl side f n ngle in stndrd psitin lies in qudrnt II f the crdinte grid. The rdin mesure f this ngle culd be π 4π 7π π () () () (4) 6 0) Which f the fllwing ngles is cterminl with? () - () 4 () (4) - ) If sin nd cs < 0, in which qudrnt des terminte? () I () II () III (4) IV
4 ) Kelly buys lrge circulr pizz tht is divided int eight equl slices. She mesures lng the uter edge f the crust frm ne piece nd finds it t be inches. Wht is the dimeter f the pizz t the nerest inch? () 4in () 4in () 7in (4) 8in ) Given tht ngle A is third qudrnt ngle nd the tngent f the ngle is equl t 4, which f the fllwing sttements is nt true? () cs A () 4 sin A () ct A (4) 4 sec A 4) In the ccmpnying digrm, circle O is unit circle. Which functin des the length f line segment PQ represent? () cs () sin () ct (4) tn ) Which f the fllwing is the reference ngle f 0? () -0 () -40 () 0 (4) 0 6) If csc, wht is the vlue f sin? () () () - (4) 7) Wht is 08 cnverted t rdins in terms f π? () 6 π () π () π 6π (4) 8) If ct( 0) tn(4), then vlue f is () 0 () 40 () 0 (4) 0
5 SOLVING TRIG EQUATIONS Steps fr Slving Trig Equtins: ) Slve the equtin by fctring (if necessry). ) Circle the intervl nd in wht mesure they wnt the nswers in. ). Find the Reference Angle (qud ),. Determine ther qudrnt ngles needed using: All Students Tke Clculus S A b. If sin r cs is 0,, -: Use the Unit Circle t find ll mesures. ( specil ngles n is) T C Remember if sin r cs is utside the UNIT CIRCLE BOUNDARY there will be n ngle Mesure. (errr messge). Tn will wrk fr ll vlues. ( N errr messges) 4) Mke sure yu nswer it the wy they sked fr it (wht yu circled in step ) Substitutins t use fr Simplifying Trig Epressins: Duble Angle Substitutins: cs cs sin cs sin cs cs sin sin cs Pythgren Identity: sin + cs cs sin sin cs 9) Find, t the nerest degree the slutin set f tn + tn 8 in the intervl 0 < ) Find ll vlue f in the intervl 0 < 60 tht stisfy the equtin cs cs 0 ) The epressin sin + cs cs is equivlent t () csc () cs tn () sec (4) sin cs tn sin ) The epressin is equivlent t cs cs () cs () () sin (4) cs
6 TRIG APPLICATIONS Hw t drw nd lbel tringle: A c b Use uppercse letters fr the verte. Use lwercse letters fr the side ppsite tht verte. B C Are f Tringle: K bsinc (need SAS set up) When t use: When the questin sks fr the re r the re f tringle is given. Lw f Csines: b + c bccsa When t use: ( side-ngle reltinship in ) When the questin dels with sides nd ne ngle. Remember: A is the ne ngle, therefre is the side crss frm tht ngle Hw t drw nd lbel frces: Lw f Sines: sina b sinb c sinc When t use: ( side-ngle reltinships in ) When the questin dels with sides nd ngles. When the questin sks hw mny distinct tringles cn be drwn. There my be 0 tringles: if yu get n errr in clcultr when finding the secnd ngle. Be creful when lbeling ny ngle given t yu r when sked t find certin ngle, mke sure yu red the prblem nd lbel crrectly! Resultnt DOES NOT cut the ngle in hlf! There my be tringle: if yu cn find the secnd ngle nd the third ngle. There my be tringles: Hving mde tringle lredy, if yu cn use the supplement f the secnd ngle nd still find third ngle. ) T the nerest tenth f squre centimeter, wht is the re f the prllelgrm belw? () 4.8 () 69. () 09.6 (4) 6.8 4) In ABC, 9, c 0, nd m A. Which sttement cn be used t find the vlue f C? () 0 sin69 sinc () 9 0 sin sinc 9 () 9sin69 sinc (4) 0 0 sin C 9
7 ) Hw mny distinct tringles cn be cnstructed if AC, BC 8, nd m A 6? () () () (4) 0 6) Al is stnding 0 yrds frm mple tree nd 0 yrds frm n k tree in the prk. His psitin is shwn in the ccmpnying digrm. If he is lking t the mple tree, he needs t turn his hed 0 t lk t the k tree. Hw fr prt re the trees? () 6. yrds ()7 yrds () 70 yrds (4) 8. yrds
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