Pre-Calculus PAP/GT Introducing Trigonometry Packet #1

Transcription

1 Pre-Calculus PAP/GT Intrducing Trignmetry Packet #1

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3 Eÿqtten Functins? l What is a functin? 2. Name as many functins as yu can remember. (If yu can't remember the name, can yu graph r write an equatin f it?) 3. Which f the functins d yu think was the mst difficult? 4. Which f the functins d yu think was the easiest? 1.6 & 1.7 Paren Funcfins & Transfrmatins Parent Functins: Knw all Parent Functins frm Algebra II including Dmain, Range, Even r dd, Symmetry Vertical shift: h(x) = f(x) + c and Hrizntal shift: h(x) = f(x+c) and Vertical Reflectin (ver the x axis): h(x) = fix) c h(x) = f(x-c) h( ) = fix) Hrizntal Reflectin (ver the y-axis): h(x) = f( x) Vertical expansin (stretch) r cmpressin : h(x) = f(x) Hrizntal expansin (stretch) r cmpressin : h(x) = f(cx) 1

4 Name: Parent Functins Withut a calculatr, fr each functin belw: name the functin, sketch graph, state dmain and range using interval ntatin and state whether it is dd, even r neither. 1. f(x) = c 2. f(x) = x 3. f(x) = x2 D: D: D: R: R: R: 4. f(x)=x3 5. f(x)= x 6. f(x) k k! D: D: D: R: R: R: f(x)=-x 8. f(x)=ÿ-y 9. f (x) = Ix]] k D: R: 1. f(x) = ax where a>l D: R: 11, f(x) = ax where <a<l D: R: 12. f(x) = lgx D: R: D: R: D: R: Revised 8/12 2

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7 Hmewrk: 1.5 p #71-76, 98, 99, In Exercises , determine whether the functin is even, dd, r neither. Then describe the symmetry h(x)=x g(x)=x3-5x f(t) = t2 + 2t g(s) = 4s2/3 True r False? Determine whether the statement is true r false. Justify yur answer. 98. It is pssible fr an dd functin t have the interval [, ) as its dmain. 99. If f is an even functin, determine whether g is even, dd, r neither. Explain. (a) g(x) = -f(x) (c) g(x) = f(x)- 2 (b) g(x) = f(-x) (d) g(x) = f(x- 2) Think Abut lt. In Exercises , find the crdinates f a secnd pint n the graph f a functin f if the given pint is n the graph and the functin is (a) even and (b) dd. 11. (-3,4) 12. (--ÿ,-7) 13. (4,9) 14. (5,-1) 5

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9 Name: Date: Perid: Pre Calculus Degree/Radian ActivityJ Divide the tp f the circle int 3 increments frm t 36. Start with at the right side f the diameter and measure cunter-clckwise, Draw a line frm the center f the circle t each f the 3 increment marks yu made n the circle. Write each degree measure at its crrespnding spt n the circle = 2. 6= 3. 9= = = = = = = i. 3 = ll. 33 = = f a semicircle f a semicircle f a semicircle f a semicircle f a semicircle f a semicircle f a semicircle f a semicircle f a semicircle f a semicircle f a semicircle f a semicircle Divide the tp f the circle int 45 increments frm t 36. Start with at the right side f the diameter and measure cunter-clckwise. Draw a line frm the center f the circle t each f the 45 increment marks yu made n the circle. Write each degree measure at its crrespnding spt n the circle = 2. 9= = = = = = = f a semicircle f a semicircle f a semicircle f a semicircle f a semicircle f a semicircle f a semicircle f a semicircle Fill in the blanks with what fractin f the semicircle each angle represents. 7

10 What is a Radian? Any item can be used as a unit f measure. The width f the classrm culd be measured in inches, feet, meters r even miles. If I asked yu hw many erasers wide the rm is r hw many ceiling tiles wide it is, the eraser and the ceiling tile becme the unit f measure. When measuring arcs and angles f circles, the degree is ne pssible unit f measure. The circle is simply divided int 36 equal parts and each part is a de_ÿ. Anther way f dividing up a circle is int 4 equal parts. Each part is called a gradian. The third way f dividing up a circle is int 'radius length' arcs. Each part is called a radian. Yu will be discvering "What is a Radian" in the fllwing activity. Prcedure: 1. abel the center f the circle C. 2. Thrugh C draw the hrizntal diameter. 3. abel the right endpint f the diameter 4. ay the pipe cleaner alng the radius f the circle. Mark the 'radius length' nt the pipe cleaner. This is yur unit f measure. 8

11 5. Starting at, curve the pipe cleaner alng the circle itself and mark ff the first 'radius length'. Cntinue marking the 'radius lengths' nt the circle, but d ntg past 18. Accuracy is very imprtant! 6. Hw many ÿ 'radius lengths' fit nt the semicircle? 7. Abut what fractin f the pipe cleaner wuld be needed t cmplete the semicircle? 8. If yu think that abut f the pipe cleaner wuld cmplete the semicircle, then yu measured ve_ey well! What is the decimal value f ÿ_ t the nearest hundredth? 9. Thus, hw many 'radius lengths' fit nt the semicircle? Mixed number Imprper fractin Decimal What symbl is cmmnly used fr this value? 1. Using the infrmatin frm #9, hw many 'radius lengths' wuld fit nt the whle circle? Mixed number Imprper fractin Decimal What symbl is cmmnly used fr this value? 11. Every 'radius length' marked n the circle is an arc length crrespnding t an angle measure ne radian. Every semicircle is radii in length, r radians in angle measure. A central angle f I radian intercepts an arc f length f 12. Every cmplete circle is r radians in measure. 13. With a straight edge, cnnect the center f the circle t the first radian mark n yur circle. The measure f the central angle is ne radian. With yur prtractr, measure this angle as accurately as pssible. It is ÿ ***A ne radian anÿ;le intercepts an arc f ne radius length.*** 14. Since the measure f a ne radian angle is abut 57.3, what is the measure f a 2 radian angle? 15. Hw many radians (in decimal frm) make up a semicircle? Multiply this answer by 57.3 Yur answer shuld be very clse t Find the 7f key n yur calculatr. Nw multiply 57.3 by 7f. What d yu get?. Why is this answer mre accurate than the answer fr #15? 17. In yur wn wrds, define an angle f ne radian. (Be sure t use cmplete sentences.) 9

12 Fractinal part f semicircle Degrees Radians 1 semicircle ] f a semicircle 4 2 f a semicircle 4 3 f a semicircle 4 4 f a semicircle 4 5 f a semicircle 4 6 f a semicircle 4 7 f a semicircle 4 8 f a semicircle 4 Fractinal part f semicircle Degrees Radians 1 semicircle ]- f a semicircle 6 _2 f a semicircle 6 3_f a semicircle 6 4 f a semicircle 6 _5f a semicircle 6 6f a semicircle 6 "7 f a semicircle 6 8 f a semicircle 6 _9 f a semicircle 6 ] f a semicircle 6 ]._ÿ] f a semicircle 6 12 f a semicircle 6 1

13 rÿ -8 +ÿ ÿ ÿ6.ÿ 6 CD ÿ.ÿ ÿ ÿ II 1",1 +'ÿ ÿ1 8 "ÿ.ÿ _ÿ.ÿ qÿ )! g II ÿ rÿ : 6 ÿ : ÿ 11

14 rÿ.ÿ rÿ D,-d 8 ).) A ÿ ÿ.ÿ ÿd m <D ÿ I1 II e-i m ÿ ÿ rÿ dÿ tÿ < < 12

15 v) > 4-- J 5-9,.t--,+2_ ul t') 41 - E %= ) ) If) U ', U v) D "! tÿ Z (ÿ, ) rÿ 9 u ('ÿ, v) vi +- ixl p,l tÿ. ).ÿ > k3 tÿ 13

16 Sectin 4.1 Radian and Degree Measure 29 In Exercises 7-12, determine the quadrant in which each angle lies. (The angle measure is given in radlans.) 77r 117r 9ÿr 7, (a) 7 (b) y a. (a) y (b) -8- qr 9.(a)-]ÿ (b)-2 lltr 1. (a) - l (b) (a) 3.5 (b) (a) 6.2 (b) In Exercises 13-16, sketch each angle in standard psitin, 57r 2ÿ- 7 r 5'r 13. (a) -ÿ- (b) --ÿ- 14. (a) --ÿ (b) -ÿliar 15. (a) ÿ (b) (a) 4 (b) 7,rr In Exercises 17-2, determine tw cterminal angles (ne psitive and ne negative) fr each angle. Give yur answers In radians. 1% (a) = 2ÿ (b) = -Eÿ ÿr 2ÿr 2. (a) = --- (h) In Exercises 21-24, find (if pssible) the cmplement and supplement f each angle. r 37r 22. (a) 7r 117r 21. (a) 7 (b) -ÿ- iÿ (b)=7ÿ 23, (a) 1 (b) (a) 3 (b) 1.5 In Exercises 43-46, find (if pssible) the cmplement and supplement f each angle. 43, (a) 18 (b) 115" 44, (a) 3 (h) 64" 45, (a) 79 (b) 15 46, (a) 13 (h) 17 In Exercises 47-5, rewrite each angle in radian measure as a multiple f ÿr. (D nt use a calculatr.) 47. (a) 3 (h) 15" 48. (a) 315 (b) 12<' 49. (a) -2 (b) -24" 5, (a) -27 (b) 144ÿ In Exercises 51-54, rewrite each angle in degree measure, {D nt use a calculatr,) ÿ 7.n" 7"tr ÿr 51, (a) --- (b) -g- 52, (a) (b) 11ÿ" 54. (a) lllr 34ÿr 53. (a) ÿ (b) 3 ÿ (b) 1"-5" In Exercises 55-62, cnvert the angle measure frm degrees t radians, Rund t three decimal places , W " , -.83" In Exercises 63-7, cnvert the angle measure frm radians t degrees. Rund t three decimal places. 63. ÿ 64. 5ÿ _ÿ ÿ , -4.2ÿr 68, 4.87r In Exercises 79-82,find the angle in radians, 79. 8, 29 In Exercises 31-34, determine the quadrant In which each angle lies. 31, (a) 13" (b) 285" 32. (a) 8.3" (b) 257"3' 33. (a) - 137'5' (b) -336" 34. (a) -26" (b) -3.4" In Exercises 35-38, sketch each angle in standard psitin. 35, (a) 3" (h) 15" 36. (a) -27" (b) -12" 3% (a) 45" (h) 48" 38, (a) -75" (b) -6" In Exercises 39-42, determine tw cterminal angles (ne psitive and ne negative) fr each angle. Give yur answers In degrees. 39. (a) / (b) = 45 -ÿ In Exercises 83-86, find the radlan measure f the central angle f a circle f radius r that intercepts an arc f length s. Radius r Arc ength s inches 6 inches In Exercises 87-9,find the length f the arc n a circle f radius r intercepted by a central angle e. Radius r Central Angle inches feet meters 1 radian In Exercises 91=94, find the area f the sectr f the circle with radius r and central angle, Radius r Central Angle qr inches "ÿ 14

17 V) "-ÿ ('q N-, E Iÿ) ọ ÿ5 v) I:ÿ.x: "ÿ Nÿ ÿ,4_._ÿ -ÿ 4- J (J eÿ v) (9 t-"._ÿ jr-.!. _ kÿ A i ÿ: + I + q5 'ÿ. g ÿ tÿ

18 HWÿ # dd, #1 13, 17; Wrksheet G (dds nly) In Exercises , cnvert each angle measure t decimal degree frm. 71 (a) 5445' (b) -1283' 73. (a) 8518'3" (b) 3325" In Exercises , cnvert each angle measure t D M' S" frm. 75. (a) 24.6 (b) (a) (b) Angular Speed A cat" is mving at a rate f 65 miles per hrn', and the diameter f its wheels is 2.5 feet. (a) Find the number f revlutins per minute the wheels are rtating. (b) Find the angulat" speed f the wheels in radians per minute. 13. inear andangular Speeds' A 7 ¼ -inch cfl'culat' pwer saw rtates at 52 revlutins per minute. (a) Find the angulat" speed f the saw blade in radians per minute, (b) Find the lineat" speed (in feet per minute) f ne f the 24 cutting teeth as they cntact he wd being cut. 17. Area A sprinkler system n a farm is set t spray water ver a distance f 35 meters and t rtate tlu'ugh an angle f 14. Draw a diagram that shws the regin that can be ha'igated with the sprinkler. Find the area f the regin. WRKSHEET G In Exercises , a wheel is rtating arund its axle. Find the angle (in radians) thrugh which the wheel turns in the given time when it rtates at the given number f revlutins per minute (rpm). Assume t > and k > ,5 minutes, 1 qgm minute, 2 apm minutes, 5 rpm minute, k rpm 77. ne end f a rpe is attached t a cfl'cular dram f radius 2 feet and the ther t a steel beatn. When the chaun is rtated, the rpe wraps arund it and pulls the bject upwm'd (see figm'e). Thrugh what angle must the dnma be rtated in rder t raise the beam 6 feet? 79. A circulat" gem" rtates at the rate f 2 revlutins per minute (qgm). a, What is the angular speed f the gem" in radians per minute? b. What is the linear speed f a pint n the gem" 2 inches fi'm the center in inches pea" minute? In feet pea" minute? 81. A tiding lawn mwer has wheels that m'e 15 inches in diameter, which are turning at 2,5 revlutins per secnd. a. What is the angular" speed f a wheel? b. Hw fast is the lawn mwer traveling in miles per hur? 83. A meny-g-rund hrse is traveling at 1 feet per secnd when the meny-g-rund is making 6 revlutins per minute. Hw fat' is the hrse fi'ln the center f the meny-g-rund? 16

19 4.2--Definitin f the Trignmetric Functins A unit circle is a circle with a radius f 1. Sine = sin = --y r X Csine = cs =- P Tangent= tan =--Y, x > x F Csecant = csc =--,y ÿ Y Secant = sec = -,x > x X Ctangent = ct -,y > Y Remember: triangles triangles sin 3 = sin 6 = sin 45 = cs 3 = cs 6 = cs 45 = tan 3 = tan 6 = tan 45 = n the Unit Circle, since the radius = 1, the trig ratis are: sin = y=y cs =-=x 1 1 y csc=-,y:i: x 1 sec=-,x, 1 x X tan =--Y,x ÿ ct = --,y, x y 17 Nte: (x,y) ÿ (cs, sin ) g- 7E, ) Tc -ÿ( 4, ) )

20 Ex 1 The terminal side f an angle cÿ ges thrugh the pint (8, 15). values f the six trignmetric functins f angle z. Find the / Nte: Any pint n the terminal side f an angle ÿ may be used and the trignmetric functins will nt change. Why? Ex. 2: The terminal side f angle fl ges thrugh the pint (-3, -4). Find cs/?. Ex 3' Find the values f the six trignmetric functins fr an angle whse measure is ÿ/2 radians -(, 1) 'ÿ9 x 18

21 Ex. 4: Suppse cÿ is in quadrant II and sin cÿ = 2/3. trignmetric functins. Find the values f the ther 5 CS (Z = tan cÿ = CSC ÿ = sec (Z = ct ÿ = Helpful memry device: "All Students Take Calculus" indicates the quadrants where the trig functins are psitive: II: sine & csecant are psitive I: all functins are psitive III: tangent & ctangent are psitive IV: csine and secant are psitive Cmplete the "sign" chart: in quadrant: sin cs tan ct sec csc II III IV 19

22 The Unit Circle Psitive: Negative: Psitive: Negative: ( ) ) Psitive: Negative: (ÿ ÿ ÿ) Psitive: Negative: 2

23 Name Wrksheet B Date All wrk t be dne n ntebk paper. Write the prblem, shw wrk, bx r highlight final answers. Fr Unit Circle angles, leave answers EXACT. therwise use a calculatr. Find the equivalent radian measure fr each angle Find the equivalent degree measure fr each angle Determine the length f the arc f a circle with the specified radius subtended by a central angle f the given measure. 8. r=3.75; = r=2.55; =72 et be a central angle f a circle f radius r and s be the length f the subtended arc. Find the arc length s. 1. r=5.6ft; =3 11. r = 5.1in; =-- 12 Prblems 12 and 13 refer t the fllwing prblem situatin: A wheel with a radius f 5 feet is rtating at 12 rpm. 12. Determine the angular speed f the wheel (in rad/sec). 13. Determine the linear speed f a pint n the wheel's circmnference (in ft/sec). Prblems 14 and 15 refer t the fllwing prblem situatin: A wheel with a radius f 2.8 feet is rtating at 6 rpm. 14. Determine the angular speed f the wheel (in rad!sec). 15. Determine the linear speed f a pint n the wheel's circumference (in fi/sec). 16. A circular saw blade has an angular speed f 15, radians per minute. a. Hw many revlutins per minute des the saw make? b. Hw lng will it take the saw t make 6 revlutins? 17. A riding lawn mwer has wheels that are 15 inches in diameter, which are turning at 2.5 revlutins per secnd. a. What is the angular speed f a wheel (in rad/sec)? b. Hw fast is the lawn mwer traveling in miles per hur? 21

24 Name; PreCal PAP/GT Date: Wrksheet C All wrk t be dne n ntebk paper. Write the prblem, shw wrk, bx r highlight final answers. All answers shuld be exact. D NT use a calculatr. Evaluate each f the fllwing: lw cs sin 27 tan - 6 sin 9 3 secl8-5 tan 36 4 csc cs 18 tan36 + 4sinl8 + 5cs218 2sec + 4ct2 9 + cs 36 sin218 + cs218 sin cs2 36 sec218-3 sin cs 18 5sin cs2 27-7tan sec sin sin 27 3 csc sin sin 27-4 sin cs csc 27 - cs27-2 sin9 +5 csl8 Find the values f the six trignmetric functins fr the angles in standard psitin having the fllwing pints n their terminal sides. 15. (-3,4) 16. (-12,-5) 17. (,2) Revised 8/213 22

25 ) J: 3 u +- (31 (9 +ÿ (9 (9 E ) J:: 3 %- E {j It ) a +ÿ ÿ 'E,ÿ 'E "ÿg +-,ÿ: 3 J: ÿ {J +.. t- 'F",_ÿ ÿ v1 -- :ÿ +ÿ ÿ Q ÿ d II Jÿ U +- C J: 4= "E E Iÿ ) =ÿ "E ÿ,.ÿ, ÿ II II II II J V) ii ii Z ÿ ÿ ÿ II II II rq

26 ÿ +ÿ ÿ ÿ x: ÿ ÿ ÿ ÿ vi +_ 4-- Eÿ ÿ ÿ E ÿ C l ÿ) N-.,ÿ ÿ ,,ÿ +- ÿ).ÿ- -- g x: % ÿ +-, ÿ1ÿ '-2' n.-- " ÿ ÿ m N +- N ÿ 4-- J 4-- ÿ ÿ ÿ ÿ,i -.c ÿ. '.+- U_,4) m "ÿ Nÿ - "13.ÿ VI 24

27 Name: PreCal PAP/GT Date: Wrksheet D Find sin if: 1. csc = 3 2. csc = ÿ 3. csc = I Find tan if: 4. ct = 2 5. ct = x/3 / 3 6. csc = -.1 Identify the quadrant(s) fr the angles satisfying the fllwing cnditins. sina>,csa< 8. sec<,csc< 9. sinp<,csp> 1. tan<,ct< 11. sin> 12. tan> IV Give the signs f the six trignmetric functins fr each f the fllwing angles, V. Decide whether the fllwing statement is pssible [YES] R" nt pssible [N/P]. 19. sin=2 2. tan/7= csca= 22. tan=1 23. sinfl+l= csc-1= sina=ÿandcsca=2 26. tan/7 = 2 and ct/7 = sinÿ = and csccÿ = VI. Find all f the ther trignmetric functins fr each f the fllwing angles. 28. cscÿ = -ÿ,a in quadrant III 29. sin/7 = 7/25,/7 in quadrant II 3. csc = 2, in quadrant II 31. ct7" = -2, y in quadrant IV 32. sin=-ÿandcs> 33. ctcÿ=ÿ8,sina> 34. tan : 3/2, csc : 1'/i3/ÿ3 25

28 _ " "U z ọ..+ II I II I ii H ÿ II -n.-+ -I -h -3 :ÿ" < 'ÿ ÿ --4- ÿ 12. m ÿ' ÿ -ÿ ÿ -< ) I' - ÿ ÿ tÿ ÿ ::5- t.ÿ ', m m ÿ ÿ ÿ ÿ ÿ. ÿ m X g- q5 H H. H '^ b ÿ -+ IA "ÿ 5 IA 5' ÿ < r. q5 -+ II "+ IA b -h 5' Q. -+. < (n 9 ÿ. us' N 5' H g.-4-.q. "3 p 26..+

29 Nÿmc: PreCal PAP/GT Date: Trignmetry Wrksheet F Draw each f the fllwing angles in standard psitin and find the reference angle x 4x 23x Find the values f the six trignmetric functins fr each f the fllwing: sin cs tan csc sec ct rd3 2. 5ÿr/ ÿr/ ÿ/ ÿ/ Revised 8/213 27

30 Name: Pre-Calculus Date: Guess My Angle Perid: 1) I am thinking f a psitive secnd quadrant angle with a 4 reference angle. What's my angle? 2) I am thinking f a negative third quadrant angle with a 4 reference angle, What's my angle? 3) I am thinking f a psitive furth quadrant angle with a 4 reference angle. What's my angle? 4) I am thinking f a negative first quadrant angle with a 1 reference angle, What's my angle? 5) I am thinking f a psitive third quadrant angle with a 1 reference angle. What's my angle? 6) 1 am thinking f a negative secnd quadrant angle with a 7 reference angle. What's my angle? 7) I amthinking f a negative fmÿh quadrant angle with a 3 reference angle. What's my angle? 8) I am thinking f a psitive first quadrant angle with an 8 reference angle. What's my angle? 9) I am thinking f a psitive secnd quadrant angle with a 55 reference angle. What's my angle? 1) I am thinking f a psitive third quadrant angle with a 15 reference angle. What's my angle? 11) I am thinking f a psitive furth quadrant angle with a 25 reference angle. What's my angle? 12) I am thinking f a negative third quadrant angle with a 75 reference angle. What's my angle? 28

31 r J Wrksheet - Trig Values Evaluate each f the fllwing. 1, sin2 12 '+ cs tan sin cs2 18 3, sin csz 27 + tan 6 4. cs2 6 + sec csc sec 3 - sin 6 + cs 21" Answer true r false fr each f the fllwing, 6, sin 3 + sin 6" = sin(3 + 6 ), sin 12 = sin 15 - sin 3 i sin 12 = sin 18". cs 6 - sin, 6 '. cs 1'8 cs 6 = 2 CS cs 15 = cs. t2 ' cs 3 - sin 12 sin 3 Find all values f the angle, where < < 36, fr which the fllwing are true sin = tan = V'3 13. 'cs = -± sin = Vÿ tan= cs = 17. ct is undefined 29

32 Trig Review 9ÿ 1) -F radians = degrees 2) If the terminal side f an angle f e radians in standard psitin passes thrugh (6,-8), then cs e = 3) Evaluate: sin2 (ÿ) + sin() + cs() = _ 4) A circular gear has a radius f 2 inches and rtates at the rate f 2 revlutins per minute. a) Find the angular speed in radians per minute. b) Find the linear speed in feet per secnd. 5) What is the range f secant? 6) Start ate=-- Mve 2Z rtatins cunterclckwise. 4' 2 Find the radian measure f the resulting angle. 3

33 Trignmetry Review (Unit 1) "" -... _, ÿ, Name the quadrant in which the terminal side f each angte lies. Cnvert radians t degrees and degrees t radians. a)-24 b) 1zr 3,. Thrugh hw many radians des the minute hand f a clck travel in 2 hurs and 2 minutes? Give the measure f each reference angle in standard psitin. a) i b) -1 c) 9_ÿ d) - 9-Kn' 2 2 Find the six trignmetmc functin values fr the fllwing. 3zÿ e) 4zc a) 45 b) 12 c) 21 d) -7 --ÿ- The terminal sme f 6 pass4 thrugh the pint (-2, -5). Find the six trignmetric functin values f 6. if cs = 3 and lies in quadrant IV., find the ther six trignmetric values f. 4 if cÿ = 12, give the crdinates f th,,,ÿ pint " "' whi,,ÿ :"ÿ ÿ'ÿ I,ÿ, the n urfft circle and the terminal side f a Give a psitive and negative cterminal angle fr 5zc 23zr a) 4 b) -62 c) d) 8 9. change 155 t radians. 1, Change 2g 15.ÿ Start at =---. Mve! rtatins cunterclckwise. Find the radian measure f the 6 2 resulting angle. 12, The terminal side f a angle/3 ges thrugh the pint (-8, 15). Find the values f the six trignmetric fu.nctins, f angle 13.! sinÿ ÿ+ 2csÿ. 3--ÿ -7 tans 2ÿ = 2 : 2 Give the range f the sine and csine functins using interval ntatin. 2 Suppse a is ÿn quadrant II and sin cÿ = -. Find cs a. 3 The circular blade n a saw has a diameter f 7.5 inches and rtates at 24 revlutins per minute. Find the angular speed in radians per secnd. Find the speed f the saw teeth (in feet per secnd) as they cntact the wd being cut. i J I 31

34 CACUATR DISCVERY WRKSHEET T set yur windw fr graphing the trig functins fr this wrksheet, use the ZM - TRIG fimctin fr the first graph and yur windw shuld be apprpriate fr the rest f the wrksheet r at least easy t adjust. 1. When wrking in degree mde, we say that theperid f the graph y = sinx is 36. What des that statement mean? a) What is the perid f y = csx? b) What is the perid f the graph y = sin2x? c) What is the perid f the graph y = sinmx? ( Hint: play arund n the calculatr with sectins a and b.) 2, When wrking in radian mde, we say that the perid f the graph y = sinx is 2 re. What des that statement mean? a) What is the perid f y = csx? b) What is the perid f the graph y = sin2x? c) What is the perid f the graph y = sinmx? 32

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