PRE-CALCULUS B FINAL REVIEW NAME Wrk ut prblems in yur ntebk r n a separate piece f paper. CHAPTER 5 Simplify each t ne trig wrd r a number: tan (1) sec sec () sin ct + 1 + cs + ( sin cs ) () sin - cs () 1 + tan sec + csc (5) π 1 - cs cs (6) sin Find the eact value f each using a sum r difference frmula: (7) cs195 π (8) tan 1 (skip #9,) (11) If cs θ = 9 and θ lies in quadrant IV, find the eact value f each: 1 cs θ (b) sin θ (c) tan θ (1) If tan θ = and θ lies in quadrant III, find the eact value f each θ cs (b) θ sin (c) θ tan : (1) Find the eact value f 7π cs 1 using a half -angle frmula. Slve each equatin fr 0 < π : (1) cs ct = cs (15) cs + = 1 sin (16) sin = sin (17) cs = cs + Use a calculatr t slve each equatin crrect t decimal places fr 0 < π :. (18) cs = 56 (19) tan =. 5
CHAPTER SIX (0) Slve the triangle: A =, a =, b = 1. (angles t the nearest degree and sides t the nearest tenth) (1) Slve the triangle: A = 9, b = 11, c = 15 (angles t the nearest degree and sides t the nearest tenth) () Slve the triangle: a = 18, b = 1, c = (angles t the nearest degree) () Find the area f the triangle with A = 1, b = 19 miles, c = 7 miles (answer t the nearest square unit) () Find the area f the triangle with a = 8 yards, b = 1 yards, c = 15 yards. (answer t the nearest square unit) (5) Give the ther main plar crdinates fr 8, 5π 6 (6) Write each plar crdinate as a rectangular crdinate. Eact answers. 7π, - (b) ( 8, π ) (7) Write each rectangular crdinate as a plar crdinate. Eact answers. Keep r and θ psitive. Use radians. ( 0, 5) - (b) (-, ) (8) Write each rectangular equatin in plar frm. Slve each fr r. 7 + y = 1 (b) + y = 9 (9) Write each plar equatin in rectangular frm. Simplify yur answers. r = 1secθ (b) r = 6csθ sinθ (0) Write the cmple number -5 + 5 i in plar frm. (1) Write the prduct f z1z if z1 = ( cs70 + i sin70 ) and z = 7( cs55 + sin55 ) Answer in plar frm. () Find ( cs80 + sin80 ) i and answer in rectangular frm i.
() Find all f the cmple cube rts f 7i and answer in rectangular frm. () If u = 5i + 7j and v = i j, find: u + v (b) u - 7v (c) u v (d) the angle, t the nearest tenth f a degree, between u and v (e) the unit vectr in the same directin as v (5) If u = 5i j, v = 5i + j, w = -i - j, = 8i + j Name the pairs f parallel vectrs (b) Name the pairs f rthgnal vectrs (6) skip (7) Tw frces, F 1 with magnitude 0 punds and directin N5 E, and F with magnitude 5 punds and directin N67 E act n an bject. Find the magnitude and the directin angle f the resultant frce. Epress bth answers t the nearest whle number. (8) A persn is pulling a wagn with a frce f punds. Hw much wrk is dne in mving the wagn 58 feet if the wagn s handle makes an angle f 5 with the grund? Answer t the nearest tenth. CHAPTER 1.9, 9.1, 9., 9., 9.5 (9) Find the distance between (, -) and (7, ) (0) Find the midpint f the line segment jining (1, 5) and (11, -1) (1) A circle has center (-6, 5) and radius 9. Give the equatin. () Give the center and radius f the circle with equatin + y - 1 + 8y + = 0. () Find the verte, fcus and directri f the parabla with the equatin ( + ) = 16( y - 6 ) () Find the equatin f the parabla with verte (, -5) and directri = (5) Find the center, vertices, c-vertices, and fci f the ellipse with the equatin ( - 7) ( y + 1) + = 1 5 9 (6) Find the standard equatin f an ellipse if the majr ais has endpints (-5, 6) and (-5, -) and the minr ais has endpints (-7, ) and (-, ).
(7) Find the standard equatin f an ellipse with equatin + y 0 + 18y 5 = 0 (8) Find the vertices, fci and asympttes f the hyperbla with equatin y - = 1 6 1 CHAPTER FOUR (9) Find the radian measure f the central angle f a circle f radius yards that intercepts an arc f length 8 yards. (50) Find the length f the arc n a circle f radius 0 feet intercepted by a central angle f Epress yur answer as an eact multiple f π. (51) Find the value f each t decimal places: π (c) csc(7) (d) ct 7 (5) Find a cfunctin with the same value as the given epressin: sec( 5 ) (b) ct π 11 (5) A twer that is 15 feet tall casts a shadw 188 feet lng. Find the angle f elevatin, θ, f the sun t the nearest degree and label yur answer. 0. 188 ft (5) Find the values f the acute angle θ t the nearest degree. sin θ =.9781 (b) tan θ = 1.55 (55) Find the values f the acute angle θ t the nearest hundredth f a radian. cs θ =.1 (b) tan θ =.567 (56) The pint (, -6) is n the terminal side f angle θ. Find the eact values f the 6 trignmetric functins f θ. (57) If tanθ = 9 and sinθ < 0, find the eact values f the ther 5 trig functins f θ
(58) Find an equatin fr each graph: (b) Fr #59: give the amplitude, perid, and phase shift. Graph 1 perid marking all imprtant and y numbers as discussed in class: (59) π y = 5cs - Fr #60: Give the amplitude & perid. Graph perids with all imprtant numbers as discussed in class: (60) y π = tan Fr #61-66: Find the eact value f each: (61) (6) 1 sin 1 (6) csc cs 1 1 5 1 cs 1 (65) ct sin 8 1 (6) tan ( 1 ) (66) π cs cs 1 (67) A plice helicpter is flying at 550 feet abve the grund. A stlen car is sighted at an angle f depressin f 55. Find the distance f the stlen car, t the nearest tenth f a ft, frm a pint n the grund directly belw the helicpter. (68) A ht-air balln is rising vertically. Frm a pint n level grund 0 feet frm the pint directly under the passenger cmpartment, the angle f elevatin t the balln changes frm 19. t 1. 7. Hw far, t the nearest tenth f a ft, des the balln rise during this perid? 0 ft.
(69) A ship is 0 miles east and 1 miles nrth f a harbr. What bearing did he take t sail frm the harbr? Answer t the nearest tenth f a degree. CHAPTER 11 Find each it. (70) + 1 6 (71) 1 7+ 6 1 (7) + + + (7) + 9 + (7) 9 9 (75) 1 1 Use the graph f f() belw t answer #76-8 (76) ff() (77) + ff() (78) ff() (79) ff() (80) True f false, f() is cntinuus at =. Eplain yur answer using the definitin f cntinuity. (81) 1 ff() (8) True f false, f() is cntinuus at = -. Eplain yur answer using the definitin f cntinuity. The End! If yu did the entire review and UNDERSTAND hw t d the prblems yu shuld get an A! Remember this ne test is 0% f yur grade.
ANSWERS: (1) cs () csc () csc () sin (5) sin (6) tan (7) 6 (8) 1 r 1+ + (11a) 1519 1681 (11b) 70 1681 (11c) 70 1519 (1a) (1b) (1c) - (1) (1) π π π 5π =,,, (15) π = (16) π 5π = 0, π,, (17) = π (18) = 1.179, 5.065 (19) = 1.891,.9907 (0) B1 = 50, C1 = 97, c1 = 18. and B =, C = 17, c = 5. (1) a = 18.9, B = 6, C = 5 () A = 55, B = 9, C = 86 () 56 sq miles () 8 sq yards (5) 7π 8, 6, 8, π 6, 11π 8, 6 (6a) ( 5,5 ) (6b) ( 8,0) (7a) π 5, (7b) π, (8a) 1 r = (8b) r = 7 (9a) = 1 (9b) + y = 6 y 7cs θ + sin θ (0) π π 5 cs + sin i (1) 8( cs15 + i sin15 ) () i () i, + i, + i 1 (b) -60i + 5j (c) 9 (d) 71. (e) 9 9 i + 9 9 j (5a) w, (5b) u, w and u,
(7) magnitude: 8 lbs. (8) 07.8 ft-punds (9) 5 θ = 8 (0) (6, -.5) (1) ( + 6) + (y 5) = 81 () center: (6, -) radius: 7 () verte: (-, 6) fcus: (-, ) directri: y = () (y + 5) = -8( ) (5) center: (7, -1) vertices: (, -1), (1, -1) c-vertices: (7, ), (7, -) fci: (, -1), (11, -1) (6) ( + 5) ( y - ) + = 1 16 (7) ( - 5) ( y + ) + = 1 (8) vertices: (6, 0), (-6, 0) (9a) fci: ( 5, 0), (5, 0) ( + ) ( - ) ( y - 6 ) y (9b) = 9 + = 1 9 asympttes: y = ± 1 6 (9).5 (50) π ft. (51) (c) 1.51 (d).8 (5) csc 8 (b) 5π tan (5) (5) 78 (b) 85 (55) 1.5 (b). (56) csθ =, sinθ =, tanθ =, secθ =, csc θ =, ct θ = 1 (57) csθ = 9 97 97, sinθ = 97 97, secθ = 97 9, csc θ = 97, ct θ = 9 (58) a) y = -sin() b) y = 6cs π -
(59) amplitude: 5 perid: π phase shift: π 6 (60) amplitude: nne perid: (61) π (6) π (6) π (6) 5 6 1 (65) 55 (66) π (67) 85.1 ft. (68) 6.9 ft. (69) N59. 0 E 70) 0 71) 5 7) 1 7) 0 7) 1 6 1 75) 16 76) 77) 78) DNE 79) 80) False. f() is discntinuus at = because the ff() = DDDDDD wwhiiiiii ff() =. Since the values dn t match, by definitin, it is discntinuus at =. 81) 1 8) TTTTTTTT. ff() = ff( ) =