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1 Name: Semester One Eam Review Pre-Calculus I. Second Nine Weeks Graphing Trig Functions: sketch the graph of the function, identif the parts being asked. 1. sin. cos( ) 1 Domain: Range: Domain: Range: Amplitude: Period: Amplitude: Period: Phase shift: Vertical slide: Phase shift: Vertical slide:. 1 sec 4. csc( ) a = b = Period: a = b = Period: Phase Shift: V. Shift: Phase shift: V. Shift: Asmptotes: Asmptotes: Domain: Range: Domain: Range: 5. tan 1 6. csc a = b = Period: a = b = Period: Phase Shift: V. Shift: Phase shift: V. Shift: Asmptotes: Asmptotes: Domain: Range: Domain: Range:

2 cos 7. sin Domain: Range: Domain: Range: Amplitude: Period: Amplitude: Period: Phase shift: Vertical slide: Phase shift: Vertical slide: Write the equation of the graph shown below Applications of trigonometric functions: Write the equation that epresses the following situations. 1. As ou ride a Ferris wheel, our distance from the ground varies sinusoidall with time. You are in the last seat filled and the Ferris wheel starts immediatel. Let t be the number of seconds that have elapsed since the Ferris wheel started. You find that it takes 5 seconds to reach the top, 57 feet above the ground, and that it makes a revolution ever 10 seconds. The diameter of the wheel is 54 feet. 14. Han notices that Luke is not feeling well; he decides to take his temperature. His bod temperature varies sinusoidall with time. 10 minutes after he started timing, it reached a high of 10 F. minutes later, it reaches its net low, 99 F. 15. Virologists find that the number of people sick with a certain disease varies periodicall. Assume that the number of sick people varies sinusoidall with time. Records stat being kept when t = 0 ears. A minimum number, 50 people have the disease when t =.5 ears. The net maimum, 50 people, occurred at t = 7.5 ears.

3 Right Triangle Applications 16. Luke Skwalker s X-Wing is coming in for a landing on Hoth. He is currentl at an altitude of km above the planets surface. The angle of depression from the plane to the ground is 6.. What is Luke s horizontal distance from the landing platform? 17. Bilbo Baggins has been offered a job to surve the height of a nearb building. From the base of the building, Bilbo measures a distance of 15 meters. From this distance, Bilbo is able to determine that the angle of elevation to the top of the cliff is 4. What is the height of the building? 18. An 1800-foot high cell phone tower is to be supported b gu wires running from the ground to the top. The angle of elevation from the ground to the top of the tower is 7. How long will each wire be? How far from the base of the tower must the wires be anchored in the ground? 19. In an emergenc dive, Captain Nemo takes his submarine down. The angle of depression with the ocean s surface is 6. If the sub goes for 100 m along its downward path, how deep will it be? What horizontal distance from its starting point? In order to avoid detection from surface ships, the sub must dive to a depth of 000m. How far must it travel along its downward path to reach a depth of 000m? Law of Sines/Cosines 0. Use the Law of Sines to find the missing parts of the triangles: a. A = 75, a = 18, b = 1 b. B = 100, C = 8, b = 1. c. B = 1, b = 45, c = Use the Law of Cosines to find the missing parts of the triangles: a. a = 55, b = 5, c = 7 b. A = 56, b = 7., c = 8 c. B = 10.5, a = 40, c = 0. A surveor measures three sides of a triangular field and gets 4 ft, ft, and 18 ft. What is the measure of the largest angle of the triangle?. Hamlet is storming a castle and needs to find the height of the parapet in order to build scaffolding high enough to go over the walls. From where he is standing, he measures the angle of elevation to be 46. He moves 0 m closer to the castle and measures the angle of elevation to be 5. Find the height of the castle walls. 4. Two planes leave an airport at the same time. Plane A travels at 750 mph, while Plane B travels at 500 mph. a. How far apart will the be after 5 hours if the angle between their paths is 75? b. After 7 hours the are 100 miles apart. What is the measure of the angle between their paths? 5. While on a secret mission to save Endor, Leia was put into space to check two satellites. As she approaches the satellites, she finds that one of them is 1 km from her and the other is 1 km. She measures the angle between the two satellites (Leia at the verte) to be 95. How far apart are the satellites? 6. Bilbo and Frodo are standing 5 miles apart when the see a hot air balloon floating over their heads. Bilbo s angle of elevation to the balloon is 14 while Frodo s angle of elevation to the balloon is 10. How high up is the balloon? 7. To avoid a deadl ion cloud, Captain Kirk must steer the Enterprise around it. He turns at an angle of 8 from his original path. He flies for awhile then turns and intercepts his original path at an angle of 65. He ended up 7 light-ears from when he left the path. How far did he travel in order to avoid the ion cloud? Area of Triangles Find the area of the following triangles: a. a = 5, b = 9, C = 14 b. b = 1, c = 1, A = 71 c. a = 4, b = 7, c = 54 d. a = 1, b = 5, c = 7 8. Evaluate the following: a. sin(arccos( )) b. arccos(sin60) c. sin-1 e. cos (arcsin ) f. arctan 1 d. cos(arccos ) g. tan( arcsin ) h. cos(arcsin 0)

4 Trigonometric Identities: Simplif the following. 9. sec (sec cos ) csc 1 0. cos sec csc. 1 tan 4. cos(-) tan csc 8. 1 cot cos 1 9. sin cos 1.. sin cot cos csc sec csc 1 6. sin tan cos cot sec sin 40. sec cos sin sec tan cot Verif Trigonometric Identities 41. cos sin + 1 = cos 4. sin + cos cot = csc 4. sin coscot csc tan 44. sec 45. sec cos sin (cos sin ) 1 sin 1 sin sin cos sin 1 cos sin cos 1 cos csc cos sin csc 48. csc csccos Simplif the following using the Trigonometric Identities. 49. cos cos 7 5 sin sin tan100 tan50 1 tan100 tan sin cos sin cos 5. cos4cos18 sin4sin18 5. sin10cos5cos10sin5 54. tan tan 1tantan 55. tan4 1tan cos 5 sin sin cos tan 1tan 59. 1sin cos sin 4 cos 4 6. tan 1 tan 6. sin 1cos cos cos10 sin cos18 1cos cos48 Simplif, then Evaluate. 68. sin75 cos15 + sin15 cos tan75 tan0 1 tan75 tan sin cos sin cos cos cos sin sin 7. sin40cos0cos40sin0 7. cos105cos15sin105cos sin0cos tan75 1tan cos sin 77. cos / cos / sin / 79. sin10 1 cos cos 40 Evaluate the eact value of each epression (No Calculators) 81. sin tan15 8. cos sin55 Solve the following: 85. sin cos tan tan cos sin sin sin 1 II. First Nine Weeks

5 Write the equation for the function that has the graph with the given characteristics. 90. Cubic translated 4 units right, reflected over the -ais, and moved units up. 91. Absolute value stretched horizontall b a scale factor of, and translated 4 units down. 9. Rational translated 5 units left, reflected over the -ais, and translated 7 units up. 9. Quadratic reflected over the -ais, stretched verticall b a factor of and shifted 1 unit down. 94. Square Root with a horizontal reflection, and shifted down units. 95. Rational Function stretched horizontall b a factor of, translated 4 units left and units up. 96. Absolute value translated right 1 units, reflected over the -ais and stretched verticall b a factor of 5. Determine if the following are Odd/Even/Neither. Also, determine if the function is smmetric about the origin/-ais/neither f ( ) f ( ) csc( ) 10. sec( ) 104. tan( ) 105. cot( ) Graph the following functions f ( ) ( ) 107. f ( ) f ( ) 100. cos( ) 101. sin( ) 108. f ( ) ( ) Random questions Draw an even function that is not a parent function Draw a function such that f ( ) f ( ). Is the function even/odd/neither? Smmetr? 11. Describe the smmetr of the function f ( m) m 4m. Simplif the following for the functions below. List an and all restrictions. Let: f() 4 g() 4 h() j() 4 g 11. (h j)() 114. j () 115. (g f)() 116. (fg)() 117. (f g h)() 118. f ( ) h 119. g f() 10. ( 4) 11. hg( 1) j For 1-16 Let: f() 1 g() 5 h() f(g()) 1. g(f()) 14. h(h()) 15. f( g (4)) 16. h f () 17. gh ( ( 4)) 4 Algebra of Functions: f() = + 5 g() = h() = 4 j() = Find f/g() and its domain 19. Find h(j()) and its domain Inverse Functions: Graph each function, restricting the Domain if necessar. Graph the inverse. Find the Inverse Algebraicall. 10. f ( ) f ( ) 4 1. f ( ) ( ) 1. 4

6 14. f ( ) f ( ) ( 1) 16. f( ) 1 5 Piecewise Functions: Graph the following: if 17. f () 1 if 18. f () if 0 1 if if f( ) 1 if 140. if 1 f ( ) if 1 1 if 1 Find the Domains of the following: 141. f( ) f ( ) f( ) f ( ) Graph the following, state which quadrant the angle lies in and find its Reference Angle A rotation of 740 clockwise terminates in which quadrant Graph the angle that has a 7 rotation counter-clockwise. 15. A sector of a circle with radius 5 has an arc length of 4. Find the measure of the central angle in radians A sector of a circle with radius 1 has an arc length of 17. Find the measure of the central angle in radians Determine the arc length of a circle of radius 9 cm intercepted b a central angle of.

7 156. Determine the areas of a sector with the following information: a. r = 5, = 10 b. r = 8.4, Change the following to degrees or radians c. r 1, Find two coterminal angles for the following (one positive, one negative) Find the eact values of the 6 trigonometric functions of the angle sin 168. cot 169. sec 170. cos 4 4 Find sin, cos, and tan for the point (, ) of the angle in standard positions (, 5) 17. (4, 4) 17. (, -10) 174. (-1, -4) Evaluate the following, if possible. Give eact answers sin sin sin(60) 178. cos sin cos cos(40) 18. sin(15) 18. sec tan cot sin( 4 ) 187. cos 19. sin sin cot cos( sec ) 190. sin cos tan Evaluate the following with a calculator. Round to three decimal places. Be sure to be in the correct mode sin tan cos sec 00. csc sin 5 0. cos 1 0. tan. 04. sec cot Find the angle measure of the angle formed b 1 6 rotation clockwise. 07. Is sin00 positive, negative, or zero? 08. If sin 5 8 in Quadrant III, determine the eact value of tan. 09. If tan 1 5 in Quadrant IV, determine the eact value of csc. Determine the values of that makes each statement true from cos sin 1 1. tan 1 1. csc 14. sin Determine the values of that makes each statement true from cot 16. sec 17. sin 18. tan cos Find the values of, where Round to two decimal places. Remember there will be two answers for each question. (With Calculator) 0. cos tan csc.745. sin cos Find the values of, where 0. Round to two decimal places. (With Calculator) 5. sec cos cot sin csc.4189