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Precalculus II

by: Amber Wuckert

Precalculus II MATH 122

Amber Wuckert
Lansing Community College
GPA 3.59


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This 9 page Class Notes was uploaded by Amber Wuckert on Tuesday October 13, 2015. The Class Notes belongs to MATH 122 at Lansing Community College taught by Staff in Fall. Since its upload, it has received 61 views. For similar materials see /class/222365/math-122-lansing-community-college in Mathematics (M) at Lansing Community College.

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Date Created: 10/13/15
1 Find the bi form 2 Find the 3 Find the 4 Find the trig form 5 Find the form 6 Find the form ANSWERS 1 cis 45 cis 135 cis 225 cis 315 2 cis 0 2 cis 72 BLATHJ22 IM dOIVRETETHE REN fourth roots of 1 Give answers in a fifth roots of 32 Give answers in trig form third roots of i Give answers in a bi form third roots of 4 4J i Give answers in square roots of 1 i Give answers in trig square roots of 3 4i Give answers in trig g 2 21 3 cis 30 7 2 2139 2 2 3 J 2 2239 cis150 2 2139 NE ME cis 270 1 2 2 i E j 4 2 cis 40 2 2 j 2 cis 160 2 cis 280 MATH 122 AND MATH 130 PERIVIUTATIONS AND COMBINATIONS II 1 In how many ways can offices of president vice president and secretary be lled from a group of 10 persons if any person can hold no more than one office 2 In how many ways can 8 children be arranged in a straight line if one particular child must be the rst one in line 3 How many 7 digit telephone numbers can be formed using the digits 0 through 9 Notice that the first digit cannot be 0 4 How many distinguishable permutations can be formed using all letter of ALABAMA OHIO 5 A lottery winner can choose 3 prizes from a total of 10 different prizes How many different ways can he select his winnings 6 How many ways may a committee of 1 foreman 2 union stewards and 2 union members be selected from a group of 5 foremen 8 stewards and 30 members 7 In how many different ways can 1 5 and 10 be distributed among 7 students if each student receives no more than one bill 8 SiX passengers get on a bus with 20 vacant seats In how many different ways can they be seated 9 How many different groups of four can be chosen from a 15 member boat club to row a 4oar yawl 10 A signal officer has 6 different colored ags If the ags are displayed by hoisting them in a vertical position how many different signals can be made using 4 ags at a time 5 at a time 6 at a time 3 or more at a time 11 Twelve students registering for a math course are to be assigned in equal numbers to three sections How many different ways can this be done ANSWERS 113399393720 213975040 MATH 122 quotINTERESTINGquot TRIG IDEN39I ITIES 5m 27 052 271 5m 127 1 In angm mangle an 7 i i 05 f not 7 DPP y 1tan2sec2 sm ir 05 1 kW 39 not 17 i 5m 7 tan 7 1 cotz adj x 05 7 7 7 1 m 39 sec 2L m f an 7 5 my x 5 5m 7 I 05 x 5an 2 sm2A25mAcosA A 11051 5052A5052Aism2A quot3 2 2 li25mA 25052A1 mi 7m 2 2 cosABcosAcosBsmAsmB tmltABgt tanAtanB cosAB cosAcosB ismAsmB l tanAtanB sm B51 cosB cosAsmB A B 1 it smABsmAcosBcosAsmB tanAB aquot a 1tanAtanB MATH 122 AND MATH 130 PERMUTATIONS AND COIVIBINATIONS I 1 A building has ve entrances In what number of ways can one enter the building and leave by a different entrance 2 With the letters of the word CHOSEN how many fourletter words can be fomied that end in a vowel 3 If each of nine boys is to receive a book how many different distributions can be made with four identical algebra books and five identical geometry books 4 How many distinct signals can be made with six ags displayed in vertical order all at one time if three are yellow two are blue and one is red 5 How many different committees of four can be chosen in a club having thirtytwo members 6 In how many different orders can four French three English and three German books be arranged on a shelf so that all the books in each language are together 7 A white die and a black die are rolled a In what number of ways can the dice show their points b How many of these show a total of seven points 8 If the digits 1 2 3 4 5 6 and 7 are used without repetitions a how many numbers each of five figures can be formed b How many end in 25 9 a How many different committees of five can be selected from 12 persons b If a certain person is to be included c If a certain person is to be excluded 10 From five black balls and six white balls how many selections of five balls can be made so that a exactly two are black b at least two are black 11 a What number of different quartets can be selected from six boys and five girls b How many of these quartets consist of two boys and two girls 12 How many numbers between 20000 and 40000 can be made with the five digits 1 2 3 4 and 5 without repeating any digit ANSWERS Solve for X y t or0 1 tanX10 2 2sinX10 3 sinx 20 4 cotx 1 B 0 5 4sin2t10 6 2tanX2cotx30 7 2cos2010 8 sin2y 2 sin y 0 9J cosxsinx0 10 2sin2XsinX10 MATH 122 TRIG EQUATIONS 11 3tan2X10 12 sing x5 sin 3 cos 3 Equations involving multiple angles Find all solutions in 0211z or 0360 13 sin202sin00 14 cos20cos010 15 4sinxcosxf 16 cos 2Xcosx 17 42005 2x 1 18239351n2X 3U 1 5 l 4 1 sm E cos g 5m t 19 ANSWERS In the following k is an integer 37 kw 135 180 k 1 4 3 1m 4 180 k 01 4 TE 5 2k3rand 2k5t 2 6 6 or 30 360 k and 150 360 k 3 No Solution 31 k d5x k 6 306 if or 30 180 k and 150 180 k kit and 7 kit 12 5 or 180 k and 60 180 k 13 0 nor 0 180 MAT H SIMPLIFYING TRIG EXPRESSIONS Slmplify the followmg trlg expressions completely m an 1 1 cotzt 55 mat sec SEE t tan t Ens t smzt Bolt 5 t E0531 sm t an 1 7 seek tanzicsczt 71 1 r coszt 1 DOE b 1 com 25 l tant ebtnnl 5m cotzt 17 mil 2 cos 7 cos anzt 05 se 1 7 cos 0 not tan 1 cott m n m r m tan r not L set can can cast smt lant cscx tan 2 2 not t 05 t not 7 coszt z 1 5m x e an tax12 smzt m can t mi ant 50521 7 1 251m cost 1111 7 cos 1 11 mi 71 27 sec 1 14 cost 5 5321 7 1 smt1 1 71 28 1 7 cost Ir anzt H 11anzt sec t soft 29 11an t 34 59 co t csczt ant 7 ant sm t com 5321 7 can m 2 smt cosL 35L sml taut cost sec 1 7 cos 1 cos 1 3L Z39mtsmt 33 1mm 51115 031 1 32 r smt cost 37 17 cost 50531 smzt 33 cos c 5m 1 ANSWERS 1 anzt 14 ant 27 cost 2 2mm 15 smt 28 csct 3 am 16 1 29 2052 4 cost 17 391 l 30 2 5 1 18 smzt 1 19 c531 6 391 31 3 20 5321 7 1 32 smtcost MATH122 Using the TI83 to Evaluate Sequences To evaluate any sequence change the MODE setting from Func to Seq then press the Y key As many as three sequences can be de ned they are named u v and w Subscripts are put inside parenthesis The value of nMin is the subscript value that begins the sequence usually 0 or 1 Enter the formula for the sequence see examples below then go to the TBLSET screen Enter values of TblStart 1 ATbl 139 set Indpnt Auto and Depend Auto You may change the value of TblStart to any index value for which the sequence is defined if you want to look at temis of the sequence further along in the list Go to the TABLE screen The values of the first few members of the sequence are given More can be found by scrolling down A graph of values can be shown by using the WINDOW settings with nMin and nMax values that are consistent with the Xmin and Xmax values It is up to the user to set the Ymin and Ymax values so the sequence values show on the screen just as it is when graphing other functions There are two type of sequences that can be evaluated on the Tl83 nonrecursive and recursive Here is an example for a nonrecursive sequence Example 1 The sequence is an where an 2 3n 1n for n 2 1 On the Y screen enter nMin 1 and un 2 3n 1quotn Use the same XT6n key that you usually use to enter x to enter the n Recursively def1ned functions also use the MODE setting of Seq Here are two examples for recursivelyde ned sequences Example 2 If a1 5 and an1 2an for n 2 1 we use the original starting value for the subscript nMin 1 but we must write un instead of anl so we subtract 1 from all subscript values in a to get the corresponding u infomiation an1 2 an becomes un 2un1 Use 2nd 7 to enter u in the formula and use the same XT6n key that you usually use to enter x to enter the n Enter unMin 539 it is still true for u as it was for al 5 Example 3 If a1 5 a2 12 and an2 an1 an for n 2 1 we use the original starting value of the subscript nMin 1 but we must write un instead of an2 so we subtract 2 from all subscript values in a to get the corresponding u information an2 an1 an becomes un un1 un2 There are two initial values so we use unMin 125 Note that the initial values for a which are 5 and 12 respectively are entered in reverse order for u MATH 122 ANGLE AND RADIAN MEASURE Find the missing part of r s t Where t is the central angle in a circle of radius r and s is the corresponding arc 2 l r4fts2ft 2 t 3 radiansr3ft 3 t60 s9quot 4 r3quott3radians 5 The minute hand of a clock is 2 ft long How many inches does its free end move in 20 minutes 6 On a circle of radius 50quot tangents are drawn at 2 points separated by an arc of length 25quot Find the angle between the two tangents 7 A car is traveling with a speed of 30 mph The tread diameter of its tires is 27quot Find the speed of rotation of its tires in radians per second in revolutions per second 8 A wheel 6 ft in diameter is rotating with a uniform angular speed of 1 radians per second Find the linear speed of a point on its rim 9 A car is traveling at a speed of 45 mph Find the angular speed of its wheel in radians per second if the diameter is 25 ft 10 What is the Earth s angular speed in degrees per hour What has this to do with time zones 11 A conveyor belt runs over a pulley at a rate of 40 feet per minute The radius of the pulley is 2 ft Find the angular speed of the pulley 12 A conveyor belt runs over a pulley at a rate of 10 meters per minute The pulley is moving at 7 revolutions per minute Find the radius of the pulley ANSWERS 1 7r 1 2 radi S 6 radlans 10 15 per hour 15 makes 1 hour 2 2 ft E 391 E 96 622 dlfference 7 9 radianssec 97V


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