CK- 12 Algebra II with Trigonometry Concepts 1
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1 1.1 Pythagorean Theorem and its Converse c = Yes 8. No 9. No 10. Yes 11. No 1. No ( b+ a)( a+ b) ( a + ab+ b ) ab + c ( ab + c ) 15. Students must provide proof. CK- 1 Algebra II with Trigonometry Concepts 1
2 1. Sine Cosine and Tangent sin N = cos N = tan N = ; sin M = cos M = tan M = x 5.14 y x 11.0 y x 8.66 y b c c.18 a a b ft km CK- 1 Algebra II with Trigonometry Concepts
3 1. Inverse Trig Functions and Solving Right Triangles x 45 y x 71 y x 7 y x 45 y x 50 y x y m B 41 m A 9 b m B 56 m A 4 c m B 40 m A 50 a 10.7 CK- 1 Algebra II with Trigonometry Concepts
4 1.4 Application Problems in. 477 m. 5 m ft ft ft 9. 9 ft 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
5 1.5 Introduction to Angles of Rotations Coterminal Angles and Reference Angles QII QIV QIII QIII QIV QIII QIV 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
6 1.6 Introduction to the Unit Circle and Radian Measure π 4 4π 11π 6 5π 7π coterminal angles: π 4 π π ; reference angle: QII 1. coterminal angles: π 5 π π ; reference angle: QII coterminal angles: 11π 1π π ; reference angle: QIV coterminal angles: 10 π π π ; reference angle: QIII 15. coterminal angles: 5π 7π π ; reference angle: QIII CK- 1 Algebra II with Trigonometry Concepts 6
7 1.7 Trigonometric Ratios on the Unit Circle Undefined CK- 1 Algebra II with Trigonometry Concepts 7
8 1.8 Reciprocal Trigonometric Functions Undefined CK- 1 Algebra II with Trigonometry Concepts 8
9 1.9 Inverse Trigonometric Functions π π 5π 4 4 π 7π 4 4 π 11π 6 6 π 5π π π 4π π π 4 4 π 7π 6 6 CK- 1 Algebra II with Trigonometry Concepts 9
10 1.10 Trigonometric Ratios of Points on the Terminal Side of an Angle 1. ( 498 ). ( 5 45 ). ( 14.9 ) 4. ( ) 5. ( ) 6. ( 1017 ) sin17 = cos17 = tan17 = csc17 = sec17 = cot17 = ( 1570 ) sin 70 = 1 cos 70 = 0 tan 70 = und csc 70 1sec 70 = und cot 70 = 0 8. ( 411 ) 9. ( 80 ) sin 1 = cos1 = tan 1 = csc1 = sec1 = cot 1 = 4 1 sin 0 = cos0 = tan 0 = csc0 = sec0 = cot 0 = 10. ( 6 15 ) sin15 = cos15 = tan15 = 1 csc15 = sec15 = cot15 = ( ) 9π sinπ = 0cos π = 1 tan π = 0csc π = undsecπ = 1cot π = und CK- 1 Algebra II with Trigonometry Concepts 10
11 1. 7π 1 4 7π 7π 7π 7π 7π 7π sin = cos = tan = 11 csc = sec = cot = ( ) sin 0.98 = cos 0.98 = tan 0.98 = csc 0.98 = sec 0.98 = cot 0.98 = π 14 4π 4π 1 4π 4π 4π 4π sin = cos = tan = csc = sec = cot = 15. ( ) sin.0 = cos.0 = tan.0 = csc.0 = 5sec.0 = 5cot.0 = 5 5 CK- 1 Algebra II with Trigonometry Concepts 11
12 1.11 Using r and θ to find a Point in the Coordinate Plane 1. ( ). ( ). ( ) 4. ( ) 5. ( ) 6. ( ) 7. ( ) 8. ( ) ( ) 11. ( 6 6) 1. ( 70) 1. ( 0 11) 14. ( 7 7 ) ( 0 0) CK- 1 Algebra II with Trigonometry Concepts 1
13 1.1 Law of Sines with AAS and ASA 1. m A= 56 a 8.7 b m C = 0 a 9.4 b 6.4. m A= 65 c 5.6 a m A= 106 a 7.8 c m B= 8 c 7.6 b m C = b 16. a m B= 55 c 7.7 b m A= 95 b 4. c m C = 10 a 7.0 c m C = 5 a 87. b feet meters CK- 1 Algebra II with Trigonometry Concepts 1
14 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 two triangles m B 61 m C 78 and c 1.4 or m B 119 m C 0 and c two triangles m B 59.6 m C 87.4 and c or m B 10.4 m C 6.6 and c one triangle m B 41 m A 87 and a no triangle 11. two triangles m B 78.1 m C 67.9 and c.1 or m B m C 44.1 and c 4.9 CK- 1 Algebra II with Trigonometry Concepts 14
15 1.14 Area of a Triangle u. 681 u. 5 u u u u u 8. 1 u u 10. The two possible measures are 5 and 145 because the sine of an angle and its supplement are equal ft 1. $97.4 CK- 1 Algebra II with Trigonometry Concepts 15
16 1.15 Law of Cosines with SAS (to find the third side) If cos90 = 0 then c a b ab = + (0) or c = a + b CK- 1 Algebra II with Trigonometry Concepts 16
17 1.16 Law of Cosines with SSS (to find an angle) CK- 1 Algebra II with Trigonometry Concepts 17
18 1.17 Heron s Formula for the Area of a Triangle and Problem Solving with Trigonometry mi. 550 ft..9 and m in mi; 0.64 mi 8. 7 m ft ft; 181 ft CK- 1 Algebra II with Trigonometry Concepts 18
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