Trigonometri KARMA TEST - 9 1. A \"#$CJSпHFO 4. A F \"#$CJSпHFO 3 _ 5 | |\"# =CJSJN 9 E [\"#] m [#$] B | |\"$ CJSJN 3D [#'] m [\"$] BC I I\"# =DN I#%I = I%$I =DN 3 C m (A%EF) = a :VLBSEBLJWFSJMFSFHÌSF \" \"#$ FOCÑZÑLPM- :VLBSEBLJWFSJMFSFHÌSF UBOaLBÀUS | |EVôVOEB #$ LBÀCJSJNEJS \" # 34 C) 2 17 \" 1 # 1 $ % 11 & 4 3 3 % 29 & 3 29 2. ,FOBSV[VOMVLMBSCJSJN CJSJNWFCJSJN 5. cos2 3π + sin2 π PMBOÑÀHFOJOÀFWSFMÀFNCFSJOJOÀFWSFTJJÀUFôFU 88 ÀFNCFSJO JOÀFWSFTJOEFOLBÀrCJSJNGB[MBES JöMFNJOJOTPOVDVLBÀUS \" 2 # - 2 2- 2 C) \" # $ % & 2 2-2 % 2+ 2 & 2 2 3. B A 60° 4 6. y F 6A D 60° E 3 B _ 9x 3 C O2 | | | |\"#$%LBSFTJOEF #& =CJSJN &$ =CJSJN ôFLJMEFLJEJLLPPSEJOBUTJTUFNJOEF PSJKJOJMF % % \" WF # OPLUBMBSO CJSMFõUJSFO EPóSV m ( AFB ) ( CEB ) = m = 60°EJS QBS¿BMBS BSBTOEBLJ B¿OO ËM¿ÐTÐ % = a m ( AOB ) #VOB HÌSF \"#' ÑÀHFOJOJO ÀFWSFM ÀFNCFSJOJO ES ZBSÀBQLBÀCJSJNEJS #VOBHÌSF DPUaLBÀUS \" 2 13 # 13 C) 13 \" 3 # 4 C) 3 % 7 & 9 & 3 2 4 3 2 34 % 39 3 1. B 2. A 3. D 99 4. D 5. $ 6. A
KARMA TEST - 10 Trigonometri 1. ( sina m cosa )2 4. sin x. cos x = 1 ifadesinin FO LÑÀÑL EFôFSJ BöBôEBLJMFSEFO 3 IBOHJTJEJS PMEVôVOBHÌSF TJO6 x + cos6YJGBEFTJOJOEFôF- \" - # $ % & SJLBÀUS \" - 1 # - $ % & 1 3 3 2. * DPUY **UBOY III. sin2x IV. cos2x 3 5. cos2a +TJOa = 5 sin x = PMEVôVOBHÌSF ZVLBSEBLJJGBEFMFS- 3π 4 EFOLMFNJOJO>0 , HBSBMôOEBLJLÌLMFSUPQMB- den haOHJsi veyaIBOHJMFSJOJOEFôFSMFSJCJSSBT- ZPOFMTBZES 2 NLBÀUS \" π # Õ C) 3π % Õ & 5π 2 22 \" :BMO[*7 # *WF** $ ***WF*7 % *WF*7 & **WF*** 3. UBO5 x =UBOY 6. 2cos2 x + 4sin2 x + 2 3 sinx.cosx = 4 EFOLMFNJOJO[-Ö Ö]BSBMôOEBLBÀLÌLÑWBS- EFOLMFNJOJO Ö BSBMôOEBLBÀLÌLÑWBSES ES \" # $ % & \" # $ % & 1. B 2. A 3. A 100 4. $ 5. B 6. $
Trigonometri <(1m1(6m/6258/$5 1. (Ë[IJ[BTWFZFSEÐ[MFNJBSBTNPMBOCJSCBT- 3. ôFLJMEFLJHJCJCJSCJMBSEPNBTBTOEB9OPLUBTO- LFUCPMDV¿FNCFSTFWJZFTJ NZÐLTFLMJóJOEFPMBO EBOBUõBIB[SMBOBOCJSPZVODVCFZB[UPQV\"WF QPUBZBMJLB¿ZMBBUõZBQZPS #OPLUBMBSBSBTOEBCJSZFSF¿BSQUSBSBLLSN[UP- QVWVSNBZB¿BMõBDBLUS 1m A 5m B 3m 3,5 m 35° 1,8 m 2m 3m 1,5 m 2,7 m #VOBHÌSF ÀFNCFSJMFCBTLFUCPMDVBSBTOEBLJ X ZBUBZV[BLMLZBLMBöLLBÀNFUSFEJS (tan35°= PMBSBLBMO[ #VOB HÌSF PZVODV \" OPLUBTOEBO LBÀ NFUSF V[BôBCFZB[UPQVÀBSQUSSTBLSN[UPQVWVSB- \" # $ % & CJMJS \" 5 # 5 C) 1 % 25 & 25 3 4 78 2. - ¿VCVóV N WF N HFOJõMJóJOEFLJ CJSCJSJOF EJL 4. \"SBMBSOEB NFUSF PMBO JLJ HË[MFNDJ õFLJMEF- ZPMMBSEBOPMVõBOLBOBMBõFLJMEFLJHJCJLBOBMEVWBS LJ HJCJ \" WF # OPLUBMBSOEB EVSNBLUBES #V TSB- JMFiEFSFDFMJLB¿PMVõUVSBDBLõFLJMEFZFSMFõUJSJMNJõ- EBÐTUMFSJOEFOHF¿FOCJSV¿Bó\"OPLUBTOEBLJHË[- UJS MFNDJMJLCJSB¿ZMB #OPLUBTOEBLJHË[MFNDJJTF MJLCJSB¿ZMBHË[MFNMFNFLUFEJS 3m i 4m L 40° 35° A 1000 m B #VOBHÌSF -ÀVCVôVOVOV[VOMVôVOVi cinsin- #VOB HÌSF VÀBôO ZFSEFO ZÑLTFLMJôJ ZBLMBöL EFOWFSFOJGBEFBöBôEBLJMFSEFOIBOHJTJEJS LBÀNFUSFEJS (tan40° = 0,84 ve tan35°= \" TJOi + 4cosi # DPTi + 4sini \" 4200 # 4300 4450 $ TFDi +DPTFDi % DPTFDi +TFDi 11 11 C) & UBOi +DPUi % 4500 11 11 & 4600 11 1. $ 2. $ 101 3. & 4. A
<(1m1(6m/6258/$5 Trigonometri 1. #JSFMFLUSJLEFWSFTJOEFOCJSTBOJZFEFHF¿FOBLNO 3. #JS BUD EÐõFZ UVóMB EVWBSEBLJ IFEFGF BUõ ZBQ- BNQFSDJOTJOEFONJLUBS NBLUBES 5ÐGFóJOJO NFWDVU LPOVNVZMB ZFS TFWJ- ZFTJOEFO N ZÐLTFLMJLUFLJ IFEFGJ WVSNBLUBES I^ t h = 220 sinc 30t + π m , t > 0 &óFS UÐGFóJOJO ZÐLTFMNF B¿TO JLJ LBUOB ¿LBSS- 6 TB ZFSTFWJZFTJOEFONZÐLTFLMJLUFLJIFEFGJWV- SBCJMNFLUFEJS õFLMJOEFNPEFMMFONJõUJS #VOB HÌSF BUD EVWBSEBO LBÀ NFUSF V[BLUB- #VOBHÌSF CVFMFLUSJLEFWSFTJOEFOHFÀFOBL- ES NO BNQFS PMNBT JÀJO FO B[ LBÀ TBOJZF HFÀNFTJHFSFLJS \" # $ % & \" π # π C) π % π & π 45 15 8 43 2. ôFLJMEFLJEËONFEPMBCOZBS¿BQNPMVQ ZFS- 4. ôFLJMEFLJHJCJBSBMBSOEBLNCVMVOBO\"WF#MJ- EFONZVLBSEBLJ\"OPLUBTOEBOLBCJOFCJOJõZB- NBOMBSOEBOJLJHFNJTSBTZMBLZõFSJEJZMFWF QMNBLUBES MJLB¿MBSMB$OPLUBTOBEPóSV¿LZPSMBS C O x 21° 30° 60° A 160 km B 12 #VOBHÌSF \"MJNBOOEBOIBSFLFUFEFOHFNJ# MJNBOOEBO IBSFLFU FEFO HFNJZF HÌSF LBÀ LN A EBIBGB[MBZPMBMNöUS 3 (sin21° = 0,36, sin9° = \" # $ % & ôFLJMEFLJ LPOVNEBZLFO EËONF EPMBQ TBBU ZËOÐ- OÐO UFSTJOF EËOEÐóÐOEF \" LBCJOJOJO ZFSEFO ZÐLTFLMJóJYNFUSFPMNBLUBES #VOBHÌSF YLBÀUS \" # $ % & 1. A 2. D 102 3. B 4. &
Trigonometri <(1m1(6m/6258/$5 1. #JSTBOBZJõFISJOEF IBWBLJSMJMJóJOJONJLUBSIBGUB- 3. 4VCËDFLMFSJÐ[FSJOEF¿BMõBO¿FWSFCJMJNDJMFSJ TV J¿JNFTBJTBBUMFSJOEFBSUNBLUB IBGUBTPOVJTF¿B- CËDFóJLPMPOJTJOJOCÐZÐNFNJLUBSOIBGUBCPZVO- MõNBPMNBEóOEBOB[BMNBLUBESN3CBõOBEÐ- DB HË[MFNMJZPSMBS U IBGUB TBZT PMNBL Ð[FSF QP- õFOIBWBLJSMJMJóJOJONJLUBSOWFSFOGPOLTJZPOBõB- QVMBTZPOEBLJTVCËDFLMFSJOJOTBZT óEBWFSJMNJõUJS P^ t h = 5000 + 2000 sinf πt p , 0 #U# 8 P^ t h = 40 + 12. sinf 2π ·f t + 13 p p 3 74 õFLMJOEFNPEFMMFOJZPS U DVNBSUFTJ HFDFTJ HFDF ZBSTOEBO TPOSBLJ HÑOTBZTPMEVôVOBHÌSF FOEÑöÑLIBWBLJSMJMJ- #VOBHÌSF CVQPQÑMBTZPOEBLJFOEÑöÑLTVCÌ- ôJJMLEFGBLBÀHÑOTPOSBÌMÀÑMNÑöUÑS DFôJTBZTLBÀODIBGUBEBHÌ[MFNMFONJöUJS \" # $ % & \" # $ % & 2. #JSEËONFEPMBQÐ[FSJOEFLJZPMDVOVOZFSEFOZÐL- 4. #JS FóJL BUõ IBSFLFUJOEF IBWB TÐSUÐONFTJ JINBM TFLMJóJOJO[BNBOBCBóMPMBSBLNPEFMMFONFTJBõB- FEJMEJóJOEFZBUBZEBBMOBOZPM óEBLJHJCJEJS R^ i h = j02. sin^ 2i h PMBSBLNPEFMMFOJS ).FUSFDJOTJOEFOZFSEFOZÐLTFLMJL g U;BNBO EL R0:BUBZEBBMOBOZPM H^ t h = 20 - 19 sin f 2πt p j0#BõMBOH¿I[ 3 i\"UõB¿T H:FS¿FLJNJJWNFTJ NT2) #VOBHÌSF U= BOOEBZPMDVOVOZFSEFOZÑL- TFLMJôJLBÀNFUSFPMVS \" # $ % & NT MJL I[MB BUMBO CJS DJTNJO ZBUBZEB N ZPMBMEôCJMJOEJôJOFHÌSFBUöBÀTLBÀSBEZBO- ES \" Õ # Õ $ π % π & π 2 34 1. B 2. D 103 3. $ 4. &
<(1m1(6m/6258/$5 Trigonometri 1. 4OFMMZBTBT õóOHFMEJóJPSUBNOLSDMLJOEJTJZ- 3. ;BNBO J¿FSJTJOEF ZËOÐ WF õJEEFUJ CFMMJ CJS EÐ[FO MF HFMJõ EPóSVMUVTVOVO OPSNBMMF ZBQUó B¿OO TJ- J¿JOEF EFóJõFO BLNB BMUFSOBUJG BLN EFOJS &WMF- OÐTÐOÐO õóOHJUUJóJPSUBNOLSDMLJOEJTJZMFHJ- SJNJ[EFLVMMBOEóN[FMFLUSJLBLNCVOBËSOFLUJS EJõEPóSVMUVTVOVOOPSNBMMFZBQUóB¿OOTJOÐTÐZ- #VBLNMBJMHJMJQPUBOTJZFMGBSL MF¿BSQNOBFõJUMFONFTJZMFFMEFFEJMFOLVSBMBEF- nir. 71PUBOTJZFMGBSL WPMU normal U;BNBO TO PMNBLÐ[FSF i1 n1 7 U =TJO ÕU i2 Asal eken GPOLTJZPOVJMFNPEFMMFONJõUJS n2 #VOBHÌSF CJSFWEFLVMMBOMBONBLJOFÀBMöUSM- ELUBOLBÀTBOJZFTPOSBQPUBOTJZFMGBSLJMLLF[ n1 . sini1 = n2 . sini2 WPMUBEÑöFS #VOB HÌSF LSDML JOEJTJ PMBO PSUBNEBO \" 1 # 1 C) 1 EJL BÀZMB DBNB HFMFO CJS öôO LSMNB BÀT 60 90 120 LBÀEFSFDFPMVS (ncam = % 1 & 1 \" # $ % & 240 360 2. #JSIBWBMJNBOOEBLJ$OPLUBTOEBCVMVOBOJOJõmLBM- 4. ôFLJMEFLJEFóJSNFOJOZBS¿BQNEJS4BBUZËOÐ- Lõ LPOUSPM LVMFTJOEFLJ HËSFWMJ $ OPLUBT IJ[BTO- OÐO UFSTJOF TBCJU I[MB IBSFLFU FEFO EFóJSNFOJO EBOLNZÐLTFLMJLUF[FNJOFQBSBMFMV¿BOCJSV¿B- Ð[FSJOEFLJ9OPLUBTOOIFSTOEFCJSTVZBHJSEJóJ óO#OPLUBTOEBO\"OPLUBTOBLBEBSPMBO HË[MFNMFONFLUFEJS)ZÐLTFLMJóJ 9OPLUBTOOZFS- LNMJLIBSFLFUJOJSBEBSMBJ[MFNFLUFEJS EFO ZÐLTFLMJóJOJ HËTUFSNFLUF PMVQ U = BOOEB ) FOZÐLTFLEFóFSJOJBMNBLUBES B 20 km A X 24 km C 3m D 36 km H % su seviyesi ( ACB | |m 1m ) = a %$ =LNPMEVôVOBHÌSF 1m cotaLBÀUS yer \" 3 # 4 C) 5 % 12 & )OJOUZFCBóMGPOLTJZPOV 4 3 12 5 ) U =BDPT CU + c õFLMJOEFUBONMBONõUS #VOBHÌSF BCDEFôFSJLBÀUS \" Õ # Õ $ Õ % Õ & Õ 1. A 2. D 104 3. & 4. A
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