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Core Connections Integrated II, 2015
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Core Connections Integrated II, 2015 View details
2. Section 5.2
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Exercise 69 Page 285

Practice makes perfect
a Here we want to relate the opposite leg and the hypotenuse to the reference angle θ. To do that we should use the sine ratio.
sin θ = Opposite/Hypotenuse By substituting the given sides and angle, we get a trigonometric equation relating the side lengths and θ.
We have the following equation for θ. sin θ = 6/9 Let's solve using the inverse sine function.
sin θ = 6/9
ReduceFrac

a/b=.a /3./.b /3.

sin θ = 2/3

sin^(-1)(LHS) = sin^(-1)(RHS)

θ = sin^(-1) 2/3
UseCalc

Use a calculator

θ = 0.72972765622...
RoundDec

Round to 2 decimal place(s)

θ ≈ 0.73
b Here we want to relate the adjacent leg and hypotenuse to the reference angle θ. To do that we should use the cosine ratio.
cos α = Adjacent/Hypotenuse

By substituting the given sides and angle, we get a trigonometric equation relating the side lengths and α.

Let's solve it using the inverse cosine function.
cos α = 5/7

cos^(-1)(LHS) = cos^(-1)(RHS)

α = cos^(-1) 5/7
UseCalc

Use a calculator

α = 0.77519337331...
RoundDec

Round to 2 decimal place(s)

α ≈ 0.78
c Here, we want to relate the opposite and adjacent leg to the reference angle θ. To do that we should use the tangent ratio.

tan β = Opposite/Adjacent By substituting the given sides and angle, we get a trigonometric equation the side lengths and β.

tan β = 7/9

tan^(-1)(LHS) = tan^(-1)(RHS)

β = tan^(-1)7/9
UseCalc

Use a calculator

β = 0.66104316885...
RoundDec

Round to 2 decimal place(s)

β ≈ 0.66
Subchapter links expand_more
arrow_right 5.2.1 Perfect Square Equations p.285-286
65
66
67
68
Perfect Square Equations 69 (Page 285)
Perfect Square Equations 70 (Page 286)
arrow_right 5.2.2 Completing the Square p.289
Completing the Square 77 (Page 289)
78
Completing the Square 79 (Page 289)
Completing the Square 80 (Page 289)
Completing the Square 81 (Page 289)
Completing the Square 82 (Page 289)
arrow_right 5.2.3 More Completing the Square p.291-292
89
More Completing the Square 90 (Page 291)
More Completing the Square 91 (Page 292)
More Completing the Square 92 (Page 292)
More Completing the Square 93 (Page 292)
More Completing the Square 94 (Page 292)
arrow_right 5.2.4 Introduction to the Quadratic Formula p.296-297
Introduction to the Quadratic Formula 100 (Page 296)
Introduction to the Quadratic Formula 101 (Page 296)
Introduction to the Quadratic Formula 102 (Page 296)
Introduction to the Quadratic Formula 103 (Page 296)
Introduction to the Quadratic Formula 104 (Page 297)
Introduction to the Quadratic Formula 105 (Page 297)
arrow_right 5.2.5 Solving and Applying Quadratic Equations p.301-304
Solving and Applying Quadratic Equations 112 (Page 301)
Solving and Applying Quadratic Equations 113 (Page 301)
Solving and Applying Quadratic Equations 114 (Page 302)
Solving and Applying Quadratic Equations 115 (Page 302)
Solving and Applying Quadratic Equations 116 (Page 302)
Solving and Applying Quadratic Equations 117 (Page 303)
Solving and Applying Quadratic Equations 118 (Page 303)
Solving and Applying Quadratic Equations 119 (Page 303)
Solving and Applying Quadratic Equations 120 (Page 303)
Solving and Applying Quadratic Equations 121 (Page 303)
Solving and Applying Quadratic Equations 122 (Page 304)
Solving and Applying Quadratic Equations 123 (Page 304)
arrow_right 5.2.6 Introducing Complex Numbers p.308-310
Introducing Complex Numbers 131 (Page 308)
Introducing Complex Numbers 132 (Page 308)
Introducing Complex Numbers 133 (Page 309)
Introducing Complex Numbers 134 (Page 310)
Introducing Complex Numbers 135 (Page 310)
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