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Problem 69
Concept Check Work each problem. What angle does the line y = √3x make with the positive x-axis?
Problem 74
Find the exact value of the variables in each figure.
Problem 76
Find the exact value of the variables in each figure.
Problem 77
Find a formula for the area of each figure in terms of s.
Problem 78
Find a formula for the area of each figure in terms of s.
Problem 6
Concept Check Match each angle in Column I with its reference angle in Column II. Choices may be used once, more than once, or not at all. See Example 1. I. II. 5. A. 45° 6. 212° B. 60° 7. C. 82° 8. D. 30° 9. E. 38° 10. F. 32°
Problem 7
Concept Check Match each angle in Column I with its reference angle in Column II. Choices may be used once, more than once, or not at all. See Example 1. I. II. 5. A. 45° 6. B. 60° 7. -135° C. 82° 8. D. 30° 9. E. 38° 10. F. 32°
Problem 10
Concept Check Match each angle in Column I with its reference angle in Column II. Choices may be used once, more than once, or not at all. See Example 1. I. II. 5. A. 45° 6. B. 60° 7. C. 82° 8. D. 30° 9. E. 38° 10. 480° F. 32°
Problem 19
Find exact values of the six trigonometric functions of each angle. Rationalize denominators when applicable. See Examples 2, 3, and 5. 300°
Problem 21
Find exact values of the six trigonometric functions of each angle. Rationalize denominators when applicable. See Examples 2, 3, and 5. 405°
Problem 24
Find exact values of the six trigonometric functions of each angle. Rationalize denominators when applicable. See Examples 2, 3, and 5. 495°
Problem 27
Find exact values of the six trigonometric functions of each angle. Rationalize denominators when applicable. See Examples 2, 3, and 5. 1305°
Problem 30
Find exact values of the six trigonometric functions of each angle. Rationalize denominators when applicable. See Examples 2, 3, and 5. -390°
Problem 31
Find exact values of the six trigonometric functions of each angle. Rationalize denominators when applicable. See Examples 2, 3, and 5. -510°
Problem 35
Find exact values of the six trigonometric functions of each angle. Rationalize denominators when applicable. See Examples 2, 3, and 5. -1860°
Problem 36
Find exact values of the six trigonometric functions of each angle. Rationalize denominators when applicable. See Examples 2, 3, and 5. -2205°
Problem 37
Find the exact value of each expression. See Example 3. sin 1305°
Problem 40
Find the exact value of each expression. See Example 3. tan(-1020°)
Problem 42
Find the exact value of each expression. See Example 3. sec(-495°)
Problem 48
Evaluate each expression. See Example 4. cot² 135° - sin 30° + 4 tan 45°
Problem 53
Determine whether each statement is true or false. If false, tell why. See Example 4. cos(30° + 60°) = cos 30° + cos 60°
Problem 56
Determine whether each statement is true or false. If false, tell why. See Example 4. cos 60° = 2 cos² 30° - 1
Problem 58
Determine whether each statement is true or false. If false, tell why. See Example 4. tan² 60° + 1 = sec² 60°
Problem 62
Find all values of θ, if θ is in the interval [0°, 360°) and has the given function value. See Example 6. cos θ = √3 2
Problem 64
Find all values of θ, if θ is in the interval [0°, 360°) and has the given function value. See Example 6. sec θ = -√2
Problem 66
Find all values of θ, if θ is in the interval [0°, 360°) and has the given function value. See Example 6. √3 cot θ = - —— 3
Problem 68
Find all values of θ, if θ is in the interval [0°, 360°) and has the given function value. See Example 6. √3 sin θ = - —— 2
Problem 70
Find all values of θ, if θ is in the interval [0°, 360°) and has the given function value. See Example 6. 1 cos θ = - — 2
Problem 76
Concept Check Does there exist an angle θ with the function values cos θ = ⅔ and sin θ = ¾?
Problem 79
Suppose θ is in the interval (90°, 180°). Find the sign of each of the following. sec(θ + 180°)