Description of the Math Accuplacer Test

Transcription

1 Descriptio of the Mth Accuplcer Test Uio Buildig Testig Ceter Room 33: Dvis Cmpus Testig Ceter Room 5: For other loctios, schedules d dditiol ifo go to Cost: Mth: $0.00 (Score Reprits: $0.00) Brig to Testig Ceter: Picture ID d W#. Clcultors re NOT llowed ut scrtch pper will e provided. Accuplcer my e tke twice yer. If you feel you will ot plce ito QL mth course or MATH 060 Trigoometry plese tke the Mth Mstery Plcemet Em. You my ot plce ito MATH 00 or elow with the Accuplcer. Arithmetic Portio 7 questios 0 poit mimum Opertios with whole umers d frctios dditio, sutrctio, multiplictio, divisio, recogizig equivlet frctios d mied umers. Opertios with decimls d percets dditios, sutrctio, multiplictio, d divisio percet prolems, deciml recogitio, frctio percet equivlecies, d estimtio prolems. Applictios d prolem solvig rte, percet, d mesuremet prolems, geometry prolems, distriutio of qutity ito its frctiol prts. Elemetry Alger Portio questios 0 poit mimum Opertios with itegers d rtiol umers computtio with itegers d egtive rtiols, the use of solute vlues, d orderig. Opertios with lgeric epressios evlutios of simple formuls, epressios, d ddig, sutrctig moomils d polyomils, the evlutio of positive rtiol roots d epoets, simplifyig lgeric frctios, d fctorig. Equtios solvig, iequlities, d word prolems solvig verl prolems preseted i lgeric cotet, geometric resoig, the trsltio of writte phrses ito lgeric epressios, grphig. College Level Mth Portio 0 questios 0 poit mimum. CLM Score of 50 to 69 plces studet i y QL Mth course (MATH 030 Cotemporry Mth, 040 Itro to Sttistics, 050 College Alger, or 080 Preclculus) or MATH 060 Trigoometry.. CLM Score of 70 to 89 fulfills QL requiremet d studet is le to register for courses tht require MATH 050 s prerequisite (MATH 050 College Alger will ot pper o trscript d o credits re ered.) 3. CLM Score of 90 or higher plces studet i MATH 0 Clculus I. Algeric opertios simplifyig rtiol lgeric epressios, fctorig d epdig polyomils, mipultig roots d epoets. Solutios of equtios d iequlities the solutio of lier d qudrtic equtios y fctorig, epdig polyomils, mipultig roots d epoets. Coordite geometry ple geometry, the coordite ple, stright lies, coics, sets of poits i ple, grphs of lgeric fuctios. Applictio d other lger topics comple umers, series d sequeces, determits, permuttios, comitios, frctios, word prolems. Fuctios d trigoometry polyomil, lgeric, epoetil, logrithmic, trigoometric fuctios.

2 5//04 Distce Accuplcer Tests Distce Accuplcer Proctor Request To tke the Accuplcer i your locl commuity:. You must e fr eough wy from Weer Stte Uiversity to qulify for the Distce Accuplcer. Outside of Uth qulifies, ut iside Uth the test will ot e set to y site etwee the Uth/Idho stte lie d the Poit of the Mouti with the eceptio of Uth Stte Uiversity i Log, UT.. Cotct locl college or uiversity testig ceter ( High Schools re ot cceptle ). Ask if they will proctor your ssessmet test. The testig ceter will eed computer with Iteret ccess. Be sure the chose proctor is willig to give test lstig ywhere from + hours. 3. Register for your desired test (uttos i right colum). 4. Your request will e utomticlly emiled to our office. Your test request c tke to 7 usiess dys to process. We will otify the proctor with the eeded iformtio for your ssessmet test. 5. There is $0.00 fee per test, pyle to Weer Stte Uiversity. This fee must e pid efore the test c e setup. Oce the test is set to the proctor the pymet is processed d o refud is give. 6. You will e otified y emil oce your test hs ee set to the proctor. 7. After you hve ee otified tht your plcemet test hs ee set to the proctor, you will hve util the ed of the moth to tke your test. After tht time the iformtio set to the proctor will o loger e vlid. Like /

3 Arithmetic Smple Questios This test mesures your ility to perform sic rithmetic opertios d to solve prolems tht ivolve fudmetl rithmetic cocepts. There re 7 questios o the Arithmetic tests, divided ito three types. Opertios with whole umers d frctios: Topics icluded i this ctegory re dditio, sutrctio, multiplictio, divisio, recogizig equivlet frctios d mied umers, d estimtig. Opertios with decimls d percets: Topics iclude dditio, sutrctio, multiplictio, d divisio with decimls. Percet prolems, recogitio of decimls, frctio d percet equivlecies, d prolems ivolvig estimtio re lso give. Applictios d prolem solvig: Topics iclude rte, percet, d mesuremet prolems; simple geometry prolems; d distriutio of qutity ito its frctiol prts A B..9 C D A B C D A..035 B C D Which of the followig is the lest? A B C D All of the followig re wys to write 5 percet of N EXCEPT: A. 0.5 N B. 5N/00 C. /4N D. 5 N 7. A soccer tem plyed 60 gmes d wo 65% of them. How my gmes did it wi? A. 94 B. 04 C. 4 D Which of the followig is closest to ? A. 80 B. 300 C.,800 D. 3, is 40% of wht umer? A..8 B. 8 C. 80 D

4 Arithmetic cot 9. Three people who work full-time re to work together o project, ut their totl time o the project is to e equivlet to tht of oly oe perso workig full-time. If oe of the people is udgeted for oe-hlf of his time to the project d secod perso for oe-third of her time, wht prt of the third worker s time should e udgeted to this project? 0. 3/3 /5 A. / B. /5 C. 4/5 D. /5 A. /3 B. 3/5 C. /6 D. /8 Elemetry Alger Smple Questios A totl of questios of three types re dmiistered i this test. The first type ivolves opertios with itegers d rtiol umers, d icludes computtio with itegers d egtive rtiols, the use of solute vlues, d orderig. The secod type ivolves opertios with lgeric epressios usig evlutio of simple formuls d epressios, d ddig d sutrctig moomils d polyomils. Questios ivolve multiplyig d dividig moomils d polyomils, the evlutio of positive rtiol roots d epoets, simplifyig lgeric frctios, d fctorig. The third type of questio ivolves trsltig writte phrses ito lgeric epressios d solvig equtios, iequlities, word prolems, lier equtios d iequlities, qudrtic equtios (y fctorig), d verl prolems preseted i lgeric cotet.. If A represets the umer of pples purchsed t 5 cets ech, d B represets the umer of s purchsed t 0 cets ech, which of the followig represets the totl vlue of the purchses i cets? A. A+B B. 5(A+B) C. 0A + 5B D. 5A + 0B. A. 7 B. 30 C. D.

5 Elemetry Alger cot 3. Wht is the vlue of the epressio + 3y 4y whe d y -4? A. -80 B. 80 C. -3 D I the figure elow, oth circles hve the sme ceter, d the rdius of the lrger circle is R. If the rdius of the smller circle is 3 uits less th R, which of the followig represets the re of the shded regio? A. R B. (R-3) C. R - 3 D. R - (R-3) 5. (3- y) A. 9 4y B y C y 6y D y y 6. If, the A. B. C. D. 7. If, the A. B. C. D. 8. If -3(+4)-5, the A. 7 B. -7 C. 7 D (5-6) - 4( - 3) A. -7 B. 7 C. - D. 0. Which of the followig epressios is equivlet to? A. 5 B. 5 C. 3 D. 3

6 College Level Mth Smple Questios The College-Level Mthemtics test mesures your ility to solve prolems tht ivolve college-level mthemtics cocepts. There re si cotet res mesured o this test: () Algeric Opertios, () Solutios of Equtios d Iequlities, (c) Coordite Geometry, (d) Applictios d other Alger Topics, (e) Fuctios, d (f) Trigoometry. The Algeric Opertios cotet re icludes the simplifictio of rtiol lgeric epressios, fctorig d epdig polyomils, d mipultig roots d epoets. The Solutios of Equtios d Iequlities cotet re icludes the solutio of lier d qudrtic equtios d iequlities, systems of equtios, d other lgeric equtios. The Coordite Geometry cotet re presets questios ivolvig ple geometry, the coordite ple, stright lies, coics, sets of poits i the ple, d grphs of lgeric fuctios. The Fuctios cotet re icludes questios ivolvig polyomil, lgeric, epoetil, d logrithmic fuctios. The Trigoometry cotet re icludes trigoometric fuctios. The Applictios d other Alger Topics cotet re cotis comple umers, series d sequeces, determits, permuttios d comitios, fctorils, d word prolems. A totl of 0 questios re dmiistered o this test... If, d, the A. B. C. D. E. 3. If , the A. B. C. D. A. B. - C. D. E. 4. The grph of which of the followig equtios is stright lie prllel to the grph of y? A. 4 y 4 B. - y C. y 4 D. + y E. - y 4 E. 5. A equtio of the lie tht cotis the origi d the poit (,) is A. y B. y C. y - D. y + E. 6. A prtmet uildig cotis uits cosistig of oe- d two-edroom prtmets tht ret for $360 d $450 per moth, respectively. Whe ll uits re reted, the totl mothly retl is $4,950. Wht is the umer of two-edroom prtmets? A. 3 B. 4 C. 5 D. 6 E. 7

7 College Level Mth cot 7. If the two squre regios i the figures elow hve the respective res idicted i squre yrds, how my yrds of fecig re eeded to eclose the two regios? 8. If log 0 3, the A. 3 0 B.,000 C. 30 A. B. C. D. 00 E. 5 5 D. E. 9. If f() + d g(), the f(g()) A. B. C. D. E. 0. If is cute gle d si, the cos A. - B. 0 C. D. E. Arithmetic: )B )A 3)C 4)C 5)D 6)A 7)B 8)C 9)C 0)C Elemetry Alger: )D )C 3)A 4)D 5)D 6)B 7)D 8)B 9)B 0)A College Level Mth: )C )E 3)E 4)C 5)A 6)E 7)C 8)B 9)A 0)D

8 Frctio Rules Specil Frctios Negtive Frctios. simplifies to.. is the sme s d. does ot simplify y further.. simplifies to 3. simplifies to is NOT the sme s 4. is udefied. Additio Sutrctio Multiplictio Divisio Ccelltio ( 0, 0, c 0). ccels to. ccels to 3. ccels to 4. ccels to 5. ccels to 6. ccels to

9 Deciml Rules Comprig. Give the decimls the sme umer of plces. (You c put zeros to the right of deciml without chgig its vlue.). Compre ech umer from the deciml to the right, decidig which deciml is lrger. Additio. Lie up the decimls with poit uder poit.. Add ech colum d rig the deciml poit stright dow ito ech swer. Crry if ecessry. You c crry to the left of the deciml poit Wrig: Do't cofuse the period t the ed of setece with the deciml poit. Sutrctio. Use zeros to give ech umer the sme umer of deciml plces. Compre the decimls to decide which is lrger.. Lie up the umers with poit uder poit. Be sure to put the lrger umer o top. 3. Sutrct, orrowig if ecessry. Brig the deciml poit stright dow to the swer Divisio y Deciml To divide umer y deciml, you must first chge the divisor to whole umer.. Mke the divisor whole umer y movig the poit to the right s fr s it will go..45).900. Move the poit i the divided to the right the sme umer of plces you moved the poit i the divisor. You my eed to dd zeros to the divided. 45) Brig the poit up i the quotiet directly ove its ew positio i the divided d divide..0 45) divided y 45 is the sme s.900 divided y.45 Divisio of Deciml y Whole Numer. Put the poit i the quotiet directly ove its positio i the divided.. Divide s you would for whole umers.

10 Deciml Rules cot. Multiplictio. Plce oe umer uder the other, lied up o the right side for esy multiplictio. Multiply.. Cout the umer of deciml plces i oth umers. (Deciml plces re to the right of the deciml poit.) 3. Coutig from the right to the left put the totl umer of deciml plces i your swer. Use zeros if you eed more plces th you hve umers ? ---> 37.7 ( deciml plce ).8 ( deciml plce ) ( deciml plces, move poit plces left) Roudig. Uderlie the digit i the plce you re roudig off to.. If the digit to the right is 5 or more, dd to the uderlied digit. 3. If the digit to the right is less th 5, leve the uderlied digit s it is. 4. Drop the digits to the right of the uderlied digit..9 to the erest teth gives. (.0)..545 to the erest hudredth gives to the erest thousdth gives to the erest oe gives to the erest hudred gives to the erest thousd gives Estimtig Use estimtig to help you check the plcemet of the deciml poit. You could roud 37.7 to 40 d.8 to 3. It's esy to multiply 3 40 so you kow your swer should e close to 0. Here's "metl mth" shortcut: Whe multiplyig umer y multiple of te, just move the deciml poit oe spce to the right for every zero ( zero, spce right) ( zeroes, spces right) (3 zeroes, 3 spces right) 0, (4 zeroes, 4 spces right) 00, ,840 (5 zeroes, 5 spces right)

11 Covertig Frctios/Decimls/Percets Rules A frctio to deciml: Divide the deomitor (the ottom prt) ito the umertor (the top prt): / A percet to deciml: Move the deciml poit two plces to the left. The, drop the percet sig. 5% 0.5 A frctio to percet: Multiply the frctio y 00 d reduce it. The, ttch percet sig. /4 00 / 00 /4 5 / 5% A deciml to percet: Move the deciml poit two plces to the right. The, ttch percet sig % A deciml to frctio: Strtig from the deciml poit, cout the deciml plces. If there is oe deciml plce, put the umer over 0 d reduce. If there re two plces, put the umer over 00 d reduce. If there re three plces, put it over 000 d reduce, d so o /00 /4 Percet Equtio: Wht percet of the totl is the prt? % T P % of the 00 studets erolled i freshm Eglish ered grde of A i the clss. How my studets ered A? E: % of 00 is wht - Trslte ito equtio ( of mes multiply ; is mes equl ) (Chge % to deciml) 4 studets ered A A percet to frctio: Put the umer over 00 d reduce. The, drop the percet sig. 5% 5 /00 /4 Percet Decrese/Icrese: Lst yer studet employmet jos pid $7.5 per hour. This yer studet employmet jos re pyig $8.45 per hour. Wht percet icrese ws give to studet employmet jos?. Fid the mout of the icrese: $ $7.5 $.0. Which (hourly py) totl received icrese? The $7.5 per hour got icresed. 3. Wht % of the totl ws the icrese? or or 6.6% icrese Plce Vlue

12 Negtive d Positive Sigs Addig Rules: Positive + Positive Positive: Negtive + Negtive Negtive: (-7) + (-) -9 Sum of egtive d positive umer: Use the sig of the lrger umer d sutrct (-7) (-9) -3 (-3) (-3) Sutrctig Rules: Negtive - Positive Negtive: (-5) (-3) -8 Positive - Negtive Positive + Positive Positive: 5 - (-3) Negtive - Negtive Negtive + Positive Use the sig of the lrger umer d sutrct (Chge doule egtives to positive) (-5) - (-3) (-5) (-3) - (-5) (-3) + 5 Multiplyig Rules: Positive Positive Positive: 3 6 Negtive Negtive Positive: (-) (-8) 6 Negtive Positive Negtive: (-3) 4 - Positive Negtive Negtive: 3 (-4) - Dividig Rules: Positive Positive Positive: 3 4 Negtive Negtive Positive: (-) (-3) 4 Negtive Positive Negtive: (-) 3-4 Positive Negtive Negtive: (-3) -4 Order of Opertios I Mthemtics, the order i which mthemticl prolems re solved is etremely importt. Rules. Clcultios must e doe from left to right.. Clcultios i rckets (prethesis) re doe first. Whe you hve more th oe set of rckets, do the ier rckets first. 3. Epoets (or rdicls) must e doe et. 4. Multiply d divide i the order the opertios occur. 5. Add d sutrct i the order the opertios occur. Acroyms to Help You Rememer Plese Ecuse My Der Aut Slly (Prethesis, Epo ets, Multiply, Divide, Add, Sutrct) BEDMAS (Brckets, Epoets, Divide, Multiply, Add, Sutrct) Big Elephts Destroy Mice Ad Sils (Brckets, Epo ets, Divide, Multiply, Add, Sutrct) Pik Elephts Destroy Mice Ad Sils (Prethesis, Epoets, Divide, Multiply, Add, Sutrct)

13 Defiitios for Properties of Mthemtics Distriutive Property The sum of two umers times third umer is equl to the sum of ech dded times the third umer. For emple ( + c) + c Associtive Property of Additio Whe three or more umers re dded, the sum is the sme regrdless of the groupig of the ddeds. For emple ( + ) + c + ( + c) Associtive Property of Multiplictio Whe three or more umers re multiplied, the product is the sme regrdless of the order of the multiplicds. For emple ( ) c ( c) Commuttive Property of Additio Whe two umers re dded, the sum is the sme regrdless of the order of the ddeds. For emple + + Commuttive Property of Multiplictio Whe two umers re multiplied together, the product is the sme regrdless of the order of the multiplicds. For emple Idetity Property of Multiplictio The product of y umer d oe is tht umer. For emple. Multiplictive Iverse of Numer The multiplictive iverse of umer, is so tht Idetity Property of Additio The sum of y umer d zero is the origil umer. For emple + 0. Additive Iverse of Numer The dditive iverse of umer, is - so tht + (-) 0. Multiplictio Property of Zero Multiplyig y umer y 0 yields 0. For emple 0 0. Additio Property of Zero Addig 0 to y umer leves it uchged. For emple + 0. Property of Equlity for Additio Property of Equlity for Additio sys tht if, the + c + c. If you dd the sme umer to oth sides of equtio, the equtio is still true Property of Equlity for Multiplictio Property of Equlity for Multiplictio sys tht if, the c c. If you multiply the sme umer to oth sides of equtio, the equtio is still true.

14 Geometry Rectgle Are Legth X Width A lw Perimeter X Legths + X Widths P l + w Trigle Are / of the se X the height / h Perimeter + + c (dd the legth of the 3 sides) Prllelogrm Are Bse X Height h Perimeter X Legths + X Widths P l + w Trpezoid Perimeter +++c Circle The distce roud the circle is circumferece. The distce cross the circle is the dimeter (d). The rdius (r) is the distce from the ceter to poit o the circle. (Pi 3.4) d r c d r A r Rectgulr Solid Volume Legth X Width X Height V lwh Surfce lw + lh + wh Agles Right Agles: 90 degrees Stright Agle: 80 degrees Complemetry Agles: Two gles the sum of whose mesures is 90 degrees Supplemetry Agles: Two gles the sum of whose mesures is 80 degrees Trigles Trigles: Sum of the iterior gles is 80 degrees Isosceles Trigle: Two equl sides; two equl gles Equilterl Trigle: Three equl sides; three equl gles Right Trigles - Pythgore Theorem: + c, where d re the mesures of the legs of the trigle d c is the hypoteuse.

15 Rtio d Proportio Rtio Emples: A rtio is compriso of two umers. We geerlly seprte the two umers i the rtio with colo (:). Suppose we wt to write the rtio of 8 d. We c write this s 8: or s frctio 8/, d we sy the rtio is eight to twelve. Jeie hs g with 3 videocssettes, 4 mrles, 7 ooks, d orge. ) Wht is the rtio of ooks to mrles? Epressed s frctio, with the umertor equl to the first qutity d the deomitor equl to the secod, the swer would e 7/4. Two other wys of writig the rtio re 7 to 4, d 7:4. ) Wht is the rtio of videocssettes to the totl umer of items i the g? There re 3 videocssettes, d items totl. The swer c e epressed s 3/5, 3 to 5, or 3:5. Comprig Rtios Emple: Emples: To compre rtios, write them s frctios. The rtios re equl if they re equl whe writte s frctios. Are the rtios 3 to 4 d 6:8 equl? The rtios re equl if 3/4 6/8. These re equl if their cross products re equl; tht is, if Sice oth of these products equl 4, the swer is yes, the rtios re equl. Rememer to e creful! Order mtters! A rtio of :7 is ot the sme s rtio of 7:. Are the rtios 7: d 4:8 equl? No! 7/ >, ut 4/8 <, so the rtios c't e equl. Are 7:4 d 36:7 equl? Notice tht 7/4 d 36/7 re oth equl to /, so the two rtios re equl. Proportio Emple: A proportio is equtio with rtio o ech side. It is sttemet tht two rtios re equl. 3/4 6/8 is emple of proportio. Whe oe of the four umers i proportio is ukow, cross products my e used to fid the ukow umer. This is clled solvig the proportio. Questio mrks or letters re frequetly used i plce of the ukow umer. Solve for : / /4. Usig cross products we see tht 4 4, so 4. Dividig oth sides y, 4 so tht.

16 Alger Bsic Properties & Fcts Arithmetic Opertios Properties of Iequlities If < the+ c< + c d c< c + c ( + c) c c If < d c> 0 the c< c d < c c c If < d c< 0 the c> c d > c c c c c Properties of Asolute Vlue c d + c c d c if 0 + d d d d if < c d d c c c c + c d + c, Trigle Iequlity c c d Distce Formul Epoet Properties If P (, y) d P (, y) re two m + m m poits the distce etwee them is m m m m 0 ( ), 0 m m m Properties of Rdicls m m,if is odd,if is eve (, ) ( ) + ( ) d P P y y Comple Numers i i i ( + i) + ( c+ di) + c+ ( + d) i ( + i) ( c+ di) c+ ( d) i ( + )( + ) + ( + ) ( + i)( i) +, 0 i c di c d d c i + i + + i i + i + i + i Comple Modulus Comple Cojugte 005 Pul Dwkis

17 Logrithms d Log Properties Defiitio y y log is equivlet to Emple 3 log 5 3 ecuse Specil Logrithms l log turl log e log log0 commo log where e.78888k Fctorig Formuls If is odd the, + + L+ + 3 ( )( L ) Solve () Divide y the coefficiet of the () Move the costt to the other side. 3 5 (3) Tke hlf the coefficiet of, squre it d dd it to oth sides Logrithm Properties log log 0 log log log r rlog Fctorig d Solvig log y log + log y log log log y The domi of log is > 0 Qudrtic Formul Solve + + c 0, 0 If If If ± 4c 4c > 0 - Two rel uequl sols. 4c 0 - Repeted rel solutio. 4c < 0 - Two comple solutios. Squre Root Property If p the ± p Asolute Vlue Equtios/Iequlities If is positive umer p p or p p < < p< p > p< or p > Completig the Squre (4) Fctor the left side (5) Use Squre Root Property ± ± 4 (6) Solve for y 3 9 ± 005 Pul Dwkis

18 Costt Fuctio y or f Grph is horizotl lie pssig through the poit ( 0, ). Lie/Lier Fuctio y m+ or f m+ Grph is lie with poit ( 0, ) d slope m. Slope Slope of the lie cotiig the two,, y is poits ( y ) d y y rise m ru Slope itercept form The equtio of the lie with slope m 0, is d y-itercept y m+ Poit Slope form The equtio of the lie with slope m, y is d pssig through the poit ( ) y y + m( ) Prol/Qudrtic Fuctio y h + k f h + k The grph is prol tht opes up if > 0 or dow if < 0 d hs verte hk,. t Prol/Qudrtic Fuctio y + + c f + + c The grph is prol tht opes up if > 0 or dow if < 0 d hs verte t, f. Fuctios d Grphs Prol/Qudrtic Fuctio y + y+ c g y y + y+ c The grph is prol tht opes right if > 0 or left if < 0 d hs verte t g,. Circle h + y k r Grph is circle with rdius r d ceter hk,. Ellipse ( h) ( y k) + Grph is ellipse with ceter ( hk, ) with vertices uits right/left from the ceter d vertices uits up/dow from the ceter. Hyperol ( h) ( y k) Grph is hyperol tht opes left d hk,, vertices right, hs ceter t uits left/right of ceter d symptotes tht pss through ceter with slope ±. Hyperol ( y k) ( h) Grph is hyperol tht opes up d hk,, vertices dow, hs ceter t uits up/dow from the ceter d symptotes tht pss through ceter with slope ±. 005 Pul Dwkis

19 Commo Algeric Errors Error Reso/Correct/Justifictio/Emple 0 0 d Divisio y zero is udefied! ( ) c c , ( 3) 9 Wtch prethesis! ( ) A more comple versio of the previous error Bewre of icorrect ccelig! + Mke sure you distriute the -! See previous error. + + d + + ( + ) ( + ) ( + ) ( + ) More geerl versios of previous three errors Squre first the distriute! See the previous emple. You c ot fctor out costt if there is power o the prethesis! Now see the previous error. c c c c c c c c c c c c 005 Pul Dwkis

20 Right trigle defiitio For this defiitio we ssume tht p 0 < q < or 0 < q < 90. opposite opposite siq hypoteuse djcet cosq hypoteuse opposite tq djcet Trigoometry Defiitio of the Trig Fuctios hypoteuse djcet hypoteuse cscq opposite hypoteuse secq djcet djcet cotq opposite Uit circle defiitio For this defiitio q is y gle. y siq y cosq y tq cscq y secq cotq y Fcts d Properties Domi The domi is ll the vlues of q tht Period c e plugged ito the fuctio. The period of fuctio is the umer, T, such tht f ( q + T) f ( q). So, if w siq, q c e y gle is fied umer d q is y gle we cosq, q c e y gle hve the followig periods. Ê ˆ tq, q Á+ p, 0, ±, ±, K Ë cscq, q p, 0, ±, ±, K Ê ˆ secq, q Á+ p, 0, ±, ±, K Ë cotq, q p, 0, ±, ±, K Rge The rge is ll possile vlues to get out of the fuctio. - siq cscq dcscq - - cosq secq dsecq - - < tq < - < cotq < q ( y, ) y si ( wq) cos( wq) Æ Æ t ( wq) Æ T csc( wq) sec( wq) y Æ Æ q cot ( wq) Æ T p T w p T w p w p T w p T w p w 005 Pul Dwkis

21 Tget d Cotget Idetities siq cosq tq cotq cosq siq Reciprocl Idetities cscq siq siq cscq secq cosq cosq secq cotq tq tq cotq Pythgore Idetities si q + cos q t q + sec q + cot q csc q Eve/Odd Formuls si - q -siq csc - q -cscq cos - q cosq sec - q secq t - q -tq cot - q -cotq Periodic Formuls If is iteger. si q + p siq csc q + p cscq ( ) ( ) ( ) ( ) cos q + p cosq sec q + p secq t q + p tq cot q + p cotq Doule Agle Formuls si q siqcosq cos cos -si t q q q ( q ) q - cos -si q tq - t q Degrees to Rdis Formuls If is gle i degrees d t is gle i rdis the p t p 80 fi t d t p Formuls d Idetities Hlf Agle Formuls si q -cos( q) cos q + cos( q) -cos( q ) t q + cos q Sum d Differece Formuls si ± sicos ± cossi cos ± coscos msisi t ± t t ( ± ) m t t Product to Sum Formuls sisi Ècos cos Î coscos Ècos cos Î sicos Èsi( ) si ( ) Î cossi Èsi( + ) -si ( -) Î Sum to Product Formuls Ê + ˆ Ê - ˆ si + si siá cosá Ë Ë Ê + ˆ Ê - ˆ si - si cosá si Á Ë Ë Ê + ˆ Ê - ˆ cos + cos cosá cosá Ë Ë Ê + ˆ Ê - ˆ cos - cos -siá si Á Ë Ë Cofuctio Formuls Êp ˆ Êp ˆ siá - q cosq cosá - q siq Ë Ë Êp ˆ Êp ˆ cscá - q secq secá - q cscq Ë Ë Êp ˆ Êp ˆ tá - q cotq cotá - q tq Ë Ë 005 Pul Dwkis

22 Uit Circle Ê Á- Ë Ê Á- Ë 3, ˆ, ˆ 5p 6 Ê 3ˆ Á-, Ë 3p 4 50 p y ( 0, ) p p 3 45 Ê 3ˆ Á, Ë p 4 Ê Á Ë p 6 30, Ê Á Ë ˆ 3, ˆ (-,0) p p (,0 ) Ê 3 ˆ Á-,- Ë 7p 6 Ê ˆ Á-,- Ë 0 5p 4 Ê 3ˆ Á-,- Ë 5 4p p ( 0, - ) 300 5p p 4 Ê 3ˆ Á,- Ë p 6 Ê ˆ Á,- Ë Ê 3 ˆ Á,- Ë For y ordered pir o the uit circle (, ) y : cosq d siq y Emple Ê5p ˆ Ê5p ˆ 3 cosá si Á - Ë 3 Ë Pul Dwkis

23 Defiitio - y si is equivlet to si y - y cos is equivlet to cos y - y t is equivlet to t y Domi d Rge Fuctio Domi Rge - y si - p p - y - y cos - 0 y p - y t - < < p p - < y < Iverse Trig Fuctios Iverse Properties - - cos cos cos cos q q ( ) ( ) ( -( ) ) -( ( q) ) -( ) -( q ) si si si si q t t t t q Alterte Nottio - si rcsi cos t - - rccos rct Lw of Sies, Cosies d Tgets c g Lw of Sies si si sig c Lw of Cosies + c -c cos + c - c c + - cos cosg Mollweide s Formul + cos ( - ) c si g Lw of Tgets - t - + t + ( -g) ( g) ( -g) ( g) - c t + c t + - c t + c t Pul Dwkis