1.1 Pythagorean Theorem and its Converse 1. 194. 6. 5 4. c = 10 5. 4 10 6. 6 5 7. Yes 8. No 9. No 10. Yes 11. No 1. No 1 1 1. ( b+ a)( a+ b) ( a + ab+ b ) 1 1 1 14. ab + c ( ab + c ) 15. Students must provide proof. CK- 1 Algebra II with Trigonometry Concepts 1
1. Sine Cosine and Tangent 1. 0.576..0777. 0.6691 4. 1 5. 0.5 6. 0.049 7. 4 sin N = cos N = tan N = ; 5 5 4 4 4 sin M = cos M = tan M = 5 5 8. x 5.14 y 6.1 9. x 11.0 y 4.66 10. x 8.66 y 10 11. b 17.60 c 1.87 1. c.18 a 6.1 1. a 15.01 b 16.56 14. 17. ft 15. 1.7 km CK- 1 Algebra II with Trigonometry Concepts
1. Inverse Trig Functions and Solving Right Triangles 1. 44. 60. 81 4. 1 5. 61 6. 0 7. x 45 y 45 8. x 71 y 19 9. x 7 y 6 10. x 45 y 45 11. x 50 y 40 1. x y 57 1. m B 41 m A 9 b 9.7 14. m B 56 m A 4 c 10.8 15. m B 40 m A 50 a 10.7 CK- 1 Algebra II with Trigonometry Concepts
1.4 Application Problems 1. 11. in. 477 m. 5 m 4. 97 ft 5. 9 6. 88 ft 7. 1 8. 97 ft 9. 9 ft 10. 1 miles O 11. The hypotenuse is always the longest side. Therefore the ratios < 1 H A and < 1. H CK- 1 Algebra II with Trigonometry Concepts 4
1.5 Introduction to Angles of Rotations Coterminal Angles and Reference Angles 1. 458 6. 115 45. 570 150 4. 1 407 5. 0 58 6. 6 714 7. 5 67 8. QII 78 9. QIV 40 10. QIII 47 11. QIII 80 1. QIV 56 1. QIII 71 14. QIV 1 15. All the angles between 0 and 90 are acute angles between the terminal side of the angle and the x-axis. CK- 1 Algebra II with Trigonometry Concepts 5
1.6 Introduction to the Unit Circle and Radian Measure 1... 4. 5. π 4 4π 11π 6 5π 7π 4 6. 40 7. 90 8. 810 9. 15 10. 150 11. coterminal angles: π 4 π π ; reference angle: QII 1. coterminal angles: π 5 π π ; reference angle: QII 4 4 4 1. coterminal angles: 11π 1π π ; reference angle: QIV 6 6 6 14. coterminal angles: 10 π π π ; reference angle: QIII 15. coterminal angles: 5π 7π π ; reference angle: QIII 6 6 6 CK- 1 Algebra II with Trigonometry Concepts 6
1.7 Trigonometric Ratios on the Unit Circle 1.. 0. 4. 5. 1 1 6. 0 7. 8. 9. 10. 11. 0 1. 1 1. 14. Undefined 15. 1 CK- 1 Algebra II with Trigonometry Concepts 7
1.8 Reciprocal Trigonometric Functions 1. 1.008. -0.1405. -1.61 4. -0.466 5. -1.1099 6. -1.5080 7. -1.966 8. -1.701 9. 10. 1 11. 1 1. 1. - 14. Undefined 15. 16. CK- 1 Algebra II with Trigonometry Concepts 8
1.9 Inverse Trigonometric Functions 1. 10.6 57.4. 84.7 75.. 9.8 7.8 4. 61.5 118.5 5. 188. 51.7 6. 50. 0. 7..80 5.6 8. 1.4 4.85 9..80 5.94 10. 1.68 4.8 11. 0.78.9 1. 0.08.06 1. 0 π 14. 15. 16. 17. π 5π 4 4 π 7π 4 4 π 11π 6 6 π 5π 6 6 18. 0 π 19. 0. 1. π 4π π π 4 4 π 7π 6 6 CK- 1 Algebra II with Trigonometry Concepts 9
1.10 Trigonometric Ratios of Points on the Terminal Side of an Angle 1. ( 498 ). ( 5 45 ). ( 14.9 ) 4. ( 411.79 ) 5. ( 4 5.0 ) 6. ( 1017 ) 4 4 5 5 sin17 = cos17 = tan17 = csc17 = sec17 = cot17 = 5 5 4 4 7. ( 1570 ) sin 70 = 1 cos 70 = 0 tan 70 = und csc 70 1sec 70 = und cot 70 = 0 8. ( 411 ) 9. ( 80 ) 4 41 5 41 4 41 41 sin 1 = cos1 = tan 1 = csc1 = sec1 = 5 41 41 5 4 5 cot 1 = 4 1 sin 0 = cos0 = tan 0 = csc0 = sec0 = cot 0 = 10. ( 6 15 ) sin15 = cos15 = tan15 = 1 csc15 = sec15 = cot15 = 1 11. ( ) 9π sinπ = 0cos π = 1 tan π = 0csc π = undsecπ = 1cot π = und CK- 1 Algebra II with Trigonometry Concepts 10
1. 7π 1 4 7π 7π 7π 7π 7π 7π sin = cos = tan = 11 csc = sec = cot = 1 4 4 4 4 4 4 1. ( 10.98 ) 1 1 1 1 sin 0.98 = cos 0.98 = tan 0.98 = csc 0.98 = sec 0.98 = cot 0.98 = 1 1 14. 4π 14 4π 4π 1 4π 4π 4π 4π sin = cos = tan = csc = sec = cot = 15. ( 4 5.0 ) 5 5 1 sin.0 = cos.0 = tan.0 = csc.0 = 5sec.0 = 5cot.0 = 5 5 CK- 1 Algebra II with Trigonometry Concepts 11
1.11 Using r and θ to find a Point in the Coordinate Plane 1. (10.4 8.00). (-16.07 19.15). (16.4-4.40) 4. (-1.5 1.9) 5. (.16 6.66) 6. (-8.88 1.45) 7. (.75 1.0) 8. (9.01-4.4) 9. 5 5 10. ( ) 11. ( 6 6) 1. ( 70) 1. ( 0 11) 14. ( 7 7 ) 15. 7 7 16. ( 0 0) CK- 1 Algebra II with Trigonometry Concepts 1
1.1 Law of Sines with AAS and ASA 1. m A= 56 a 8.7 b 10.4. m C = 0 a 9.4 b 6.4. m A= 65 c 5.6 a 1.6 4. m A= 106 a 7.8 c 59.7 5. m B= 8 c 7.6 b 41. 6. m C = b 16. a 15. 7. m B= 55 c 7.7 b 9.7 8. m A= 95 b 4. c 11.9 9. m C = 10 a 7.0 c 11.7 10. m C = 5 a 87. b 5. 11. 79 feet 1. 1.5 meters CK- 1 Algebra II with Trigonometry Concepts 1
1.1 The Ambiguous Case SSA 1. triangles. triangles. 1 triangle 4. No triangle 5. triangles 6. one triangle m B 9.4 m C 75.6 and c 10.7 7. two triangles m B 61 m C 78 and c 1.4 or m B 119 m C 0 and c 4.7 8. two triangles m B 59.6 m C 87.4 and c or m B 10.4 m C 6.6 and c 9.9 9. one triangle m B 41 m A 87 and a 76 10. no triangle 11. two triangles m B 78.1 m C 67.9 and c.1 or m B 101.9 m C 44.1 and c 4.9 CK- 1 Algebra II with Trigonometry Concepts 14
1.14 Area of a Triangle 1. 71 u. 681 u. 5 u 4. 15 u 5. 15 u 6. 94 u 7. 46 u 8. 1 u 9. 1945 u 10. The two possible measures are 5 and 145 because the sine of an angle and its supplement are equal. 11. 191.5 ft 1. $97.4 CK- 1 Algebra II with Trigonometry Concepts 15
1.15 Law of Cosines with SAS (to find the third side) 1. 18.0..0. 4.9 4. 47. 5. 15.4 6. 0.9 7. 9.1 8. 15.5 9. 0.1 10. 1.9 11. If cos90 = 0 then c a b ab = + (0) or c = a + b. 1. 0.4 CK- 1 Algebra II with Trigonometry Concepts 16
1.16 Law of Cosines with SSS (to find an angle) 1. 8. 18. 65 4. 56 5. 50 6. 1 7. 47 8. 88 9. 119 10. 6 11. 88 1. 49 CK- 1 Algebra II with Trigonometry Concepts 17
1.17 Heron s Formula for the Area of a Triangle and Problem Solving with Trigonometry 1. 0.51 mi. 550 ft..9 and 7. 4. 94 5. 8575 m 6. 88 in 7. 1.6 mi; 0.64 mi 8. 7 m 9. 87 ft 10. 185 ft; 181 ft CK- 1 Algebra II with Trigonometry Concepts 18