Chapter 10 - NCPN

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Chapter Review Lessons 10.1 and 10.2 Review Examples Student Review Exercises Solve for x. Round to the nearest tenth. Use triangle ABC to find each ratio. Use the sine ratio to solve for x. sin 28ϒ= 14 x x = 14 sin 28ϒ Use a scientific calculator to evaluate sin 28°. x ≈ 29.8 in. Lessons 10.3 and 10.4 Review Examples Solve for x. Round to the nearest tenth. 1. cos B 24 2. tan A 24 25 7 Convert each angle measure to degrees or radians as appropriate. see margin 3. 40° 4. 3 ≠ radians 4 5. The angle from the top of a tree to a point 60 feet from its base is 44°. What is the height of the tree Round the answer to the nearest tenth. 62.1 ft Student Review Exercises Graph each function. 6. y = 2cos θ, 0 ≤ θ ≤ 2π see margin 7. y = tan ≠ θ, –4.5 ≤ θ ≤ 4.5 see margin 2 Use the tangent ratio to write an equation. 4 tan x°= 10 tan x°= 04 . Use the inverse tangent function and a scientific calculator to solve for x. tan –1 (tan x°) = tan –1 0.4 x = tan –1 0.4 x ≈ 21.8° 8. A 6-ft board is leaning against a wall so that the top of the board reaches a height of 4 feet 9 inches. What is the measure of the angle formed by the board and the ground Round the answer to the nearest tenth. 52.3º 502 Chapter 10 Trigonometric Functions and Identities
Lessons 10.5 and 10.6 Review Examples Find the length, x, of the bridge across the ravine. Student Review Exercises Use the Law of Sines or the Law of Cosines to find each measure. Round to the nearest tenth. Find the missing angle of the triangle. 180º – 108º – 40º = 32º Apply the Law of Sines. sin 32° sin 40° = 18 x 18sin 40° x = sin 32° x ≈ 21.8 yd Lessons 10.7, 10.8, and 10.9 Review Examples Find the exact value of cos 105°. Write 105° as 45° + 60° and use the angle sum identity cos(A + B) = cos A cos B – sin A sin B. cos105° =cos 45° • cos60° − sin 45° • sin 60° = 2 1 2 3 • − • 2 2 2 2 = 2 − 6 4 4 = 2− 6 4 9. Find c if m∠C = 35º, a = 6, and b = 8. 4.6 10. Find m∠B if a = 18, b = 13, and m∠A = 67º. 41.7º 11. Verify the trigonometric identity sin θ tan θ = 1 – cos θ. cos θ Check students’ work; see margin for sample 12. The lengths of the sides of a triangular garden are 18 feet, 14 feet, and 10 feet. What is the measure of the largest angle of the garden Round to the nearest tenth. 95.7º Student Review Exercises Find the exact value of each expression. 13. tan 105° − 3−2 14. sin 75° 2+ 6 4 15. sin 15° 6 − 2 4 16. cos 300° 1 2 Solve each equation. 17. tan 2 θ – tan θ = 0, 0 ≤ θ < 2π 0, ≠ , ≠ , 5 4 18. sin 2 θ – 1 = 0, 0 ≤ θ < 360° 90°, 270° ≠ 4 19. sin 2 θ – 1 = cos 2 θ, 0 ≤ θ < 2π ≠ , 3 ≠ 2 2 Chapter Review 503
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Chapter 10 Contents 10.1 Right Tria
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Lesson 10.1 Right Triangle Trigonom
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Solution Use the definitions of the
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Solve for x in each right triangle.
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30. A wheelchair ramp is 20 feet lo
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Arc Length The unit circle has a ra
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Using a Calculator A scientific cal
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Find the length of the intercepted
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Lesson 10.3 Inverse Trigonometric F
Page 19 and 20: see margin After taking off, a comm
Page 21 and 22: 20. What is the angle of descent of
Page 23 and 24: The y-values on the unit circle are
Page 25 and 26: Example 2 Graphing Cosine Functions
Page 27 and 28: Activity Using a Graphing Calculato
Page 29 and 30: 25. The function y = 3sin ≠ t mod
Page 31 and 32: Ongoing Assessment In PQR, m∠P =
Page 33 and 34: Activity Ambiguous Cases Two triang
Page 35 and 36: Lesson Assessment Think and Discuss
Page 37 and 38: 23. Two points in a forest, A and B
Page 39 and 40: Lesson 10.6 Verifying Trigonometric
Page 41 and 42: Activity 2 Using the Pythagorean Id
Page 43 and 44: Lesson 10.7 Angle Sum and Differenc
Page 45 and 46: Practice and Problem Solving Use a
Page 47 and 48: Lesson 13.4 Double-Angle and Half-A
Page 49 and 50: When Trigonometric Function Values
Page 51 and 52: Practice and Problem Solving Use a
Page 53 and 54: Lesson 10.9 Solving Trigonometric E
Page 55 and 56: Use the Zero-Product Property to se
Page 57 and 58: Practice and Problem Solving Solve
Page 59 and 60: Math Labs Activity 1: The Circle of
Page 61 and 62: Activity 3: The Sine Curve of Biorh
Page 63 and 64: 3 Hold a protractor upside down so
Page 65 and 66: 3 Cale, Tammie, and Allison are mem
Page 67 and 68: 8 Bella does freelance marketing wo
Page 69: Health Occupations 13 Dmitri wants
Page 73: Standardized Test Practice Multiple
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