Vocabulary Check. 410 Chapter 4 Trigonometry
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1 40 pter 4 Trigonometr etion 4.8 pplitions n Moels You soul e le to solve rigt tringles. You soul e le to solve rigt tringle pplitions. You soul e le to solve pplitions of simple rmoni motion. Voulr ek. elevtion; epression. ering. rmoni motion. Given: 0, 0. Given: 4, tn os tn 0 tn os os 0 = sin sin sin 4.4 os os os =. Given: 7 7, 4 tn sin = tn tn sin sin 7 4. Given: 90 = , tn sin tn tn sin sin Given: =, 0 00 tn 0 rtn 0.9º = Given:, sin rsin os ros = rsin 4.8 ros 44.4 =
2 etion 4.8 pplitions n Moels 4 7. Given: os, ros 7.08º = = 8. Given:., os ros sin rsin rsin ros = 9.4 =. 9. Given:, Given: sin sin 9.4 os os = 4., os 4..8 os os tn tn 4. tn 0.7 = 40.. tn tn. tn tn 4 tn. ines 0 tn 8. meters. tn tn 4. tn tn 4 tn ines tn 7.80 feet
3 4 pter 4 Trigonometr. tn 0 0 tn 07. feet 0. tn tn feet sin sin 80 si feet 0 ft 8. tn tn 8. feet () 0. tn tn feet 0 ft () Let te eigt of te ur n te eigt of te ur n steeple. Ten, tn 0 n tn () 0 tn n 0 tn tn 4740 tn. 9.9 feet 00. sin sin 4º.8 feet. tn 7 0 rtn.. () ft 7 ft ft () tn 7 0 ft () rtn 7.8 Te ngle of elevtion of te sum is.8. 4., ,00 sin 4000,00 rsin ,00 ngle of epression ,000 mi,00 mi α ot rwn to sle
4 etion 4.8 pplitions n Moels feet 0 feet 400 feet 90 feet rtn 90.0,400 ot rwn to sle miles miles 80 feet mile,400 feet 90 feet tn 90 miles,400. () ine te irplne spee is ft se ft 7 0,00 se min min, fter one minute its istne trvelle is,00 feet. sin 8,00,00 sin ft () sin 8 0,000 7s s 0,000 7(sin 8) seons 7s 0,000 feet sin sin mile miles =,0 feet ngle of gre: rtn 0..8 nge in elevtion: sin,0,0 sin,0 sinrtn 0.. feet = tn Te plne s trvele miles. sin 8 os miles nort 709 miles est 0. () Reno is 47 sin 0 49 miles of Mimi. Reno is 47 os 0 44 miles of Mimi. () Te return eing is 80. Reno mi 0 Mimi 0 80
5 44 pter 4 Trigonometr ot rwn to sle () os nutil miles sout () t ours sin nutil miles west () fter ours, te t will ve trvele 40 nutil miles. () tn 0 ering: Distne: sin.4.9 miles 40 os miles () ering from is nutil miles from port., 8 () 90 8 ering from to : 8º () 90 4 φ γ β α 0 β tn 0 0 tn meters 4. tn 4 tn 4 ot 4. 0 tn 4 0 ering:... ering 80 rtn or 8 ot 4 ot 4 0 ot 4 0 ot 4 0 ot 4 0 ot 4 ot 4.4 kilometers Port 4 0 ip irport Plne tn. 0 tn 4 0 D 07.9 ft D 00. ft Distne etween sips: D 9. ft 0. 4 D ot rwn to sle
6 etion 4.8 pplitions n Moels 4 8. ot 0 ot 8 D 0 7 kilometers D 8.8 kilometers Distne etween towns: D kilometers 9. tn 7 ot 7 tn tn ot 7 7 H P P km 8 T D 8 T ot ot 7 ot ot 7. miles 7,04 ft 40. tn. tn 9 tn. 7 tn 9 tn. 7 7 tn 9 7 tn..0 miles tn 9 40 feet ot rwn to sle 4. L : m L : m tn rtn L 8 m 4. Te igonl of te se s lengt of. ow, we ve L 4 m tn m m m m m m rtn rtn m m rtn 9. 7 tn rtn tn 4. rtn 4.7º sin 4.9 Lengt of sie: 9.4 ines
7 4 pter 4 Trigonometr r 0 r 48. sin 0 sin 0. Lengt of sie. ines os 0 r r os 0 r r r sin sin 7. sin Distne 9.0 entimeters tn 8 rtn 0.88 r.7 tn 0 0 tn 7 os 0 0. os os 8 8. feet os f. 0.8 feet f φ 9 sin 7. feet sin feet. 0 wen t 0, 4, perio. Displement t t 0 is 0 sin t. Use sin t sine 0 wen t 0. mplitue: Tus, 4 sint. Perio: t sin. wen t 0,, perio. 4. Displement t t 0 is os t. Use os t sine wen t 0. mplitue:. 4 Tus, os 4 t os 4t. Perio: t os 0
8 etion 4.8 pplitions n Moels os 8t. () Mimum isplement mplitue 4 () () Frequen 4 os 40 4 () 8 t 8 4 les per unit of time t os 0t () Mimum isplement: () Frequen: 0 0 les per unit of time () t os 00 () Lest positive vlue for t for wi 0 os 0t 0 os 0t 0 0t ros 0 0t t sin 0t () Mimum isplement mplitue () () Frequen 0 0 les per unit of time sin sin 79t 4 () Mimum isplement: () Frequen: 79 9 les per unit of time 4 4 () t 4 sin90 0 () Lest positive vlue for t for wi 0 () 0t t 0 4 sin 79t 0 sin 79t 0 79t rsin 0 79t t Frequen sin t0. t t 0, uo is t its ig point os t Distne from ig to low Returns to ig point ever 0 seons: Perio: 7 4 os t
9 48 pter 4 Trigonometr. os t, t > 0 4 () () Perio: 8 () os t 0 wen t 4 t π π π π t. () L L L L () L L L L 0..0 sin 0. os sin 0. os sin 0. os sin 0.4 os sin 0. os sin 0. os sin 0.7 os sin 0.8 os 0.8 () L L L sin os () Te minimum lengt of te elevtor is 7.0 meters.. () n () se se ltitue re 8 8 os 0º 8 sin 0º. 8 8 os 0º 8 sin 0º os 0º 8 sin 0º os 40º 8 sin 40º os 0º 8 sin 0º os 0º 8 sin 0º os 70º 8 sin 70º 80.7 Te mimum ours wen 8. squre feet. 0 n is pproimtel () () From te grp, it ppers tt te minimum lengt is 7.0 meters, wi grees wit te estimte of prt (). 8 8 os 8 sin Te mimum of 8. squre feet ours wen os 4 sin 4 os sin 0. 90
10 etion 4.8 pplitions n Moels () verge sles (in millions of ollrs) Mont ( Jnur) () Perio: Tis orrespons to te monts in er. ine te sles of outerwer is sesonl, tis is resonle. t () ift: os t t 8. os verge sles (in millions of ollrs) Mont ( Jnur) ote: noter moel is 8. sin t Te moel is goo fit. () Te mplitue represents te mimum isplement from verge sles of 8 million ollrs. les re gretest in Deemer (ol weter ristms) n lest in June. 9. t. Flse. ine te tower is not etl vertil, rigt tringle wit sies 9 feet n is not forme.. Flse. One perio is te time for one omplete le of te motion. 7. o. 4 mens 4 est of nort. 8. eronutil erings re lws tken lokwise from ort (rter tn te ute ngle from nort-sout line). 9. m 4, psses troug, 70. Liner eqution m troug , 0 7. Psses troug, n, 7. Liner eqution troug n m m ,, 4
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