University:
Felician University
Course:
MATH-002 | Basic Math Skills-Algebra
Academic year:

2019
Views:

263

Pages:

3
Author:

StellarStrategist

Name: Key Date: Period: Radian Measure Homework Problems 1-8, write each measure in radians. Express your answer in terms of π. 1. 60° 60 * π/180 = π/3 2. 135° 135 * π/180 = 3π/4 3. -30° -30 * π/180 = -π/6 4. 75° 75 * π/180 = 5π/12 5. 20° 20 * π/180 = π/9 6. 300° 300 * π/180 = 5π/3 7. 160° 160 * π/180 = 8π/9 8. 220° 220 * π/180 = 11π/9 Problems 9-16, write each measure in degrees. Round your answer to the nearest degree, if necessary. 9. 2π 2π * 180/π = 360° 10. 2π/3 2π/3 * 180/π = 120° 11. 4π/9 4π/9 * 180/π = 80° 12. 4.71 radians 4.71 * 180/π ≈ 270° 13. 15π/2 15π/2 * 180/π = 1350° 14. 1 radian 1 * 180/π ≈ 57° 15. 11π/10 11π/10 * 180/π = 198° 16. 3π/5 3π/5 * 180/π = 108° Problems 17-22, for each measure θ of an angle in standard position is given. Find the exact values of cos(θ) and sin(θ). 17. 5π/3 5π/3 * 180/π = 300° cos(5π/3) = 1/2 sin(5π/3) = -√3/2 18. 3π/2 3π/2 * 180/π = 270° cos(3π/2) = 0 sin(3π/2) = -1 19. 7π/6 7π/6 * 180/π = 210° cos(7π/6) = -√3/2 sin(7π/6) = -1/2 20. -2π/3 -2π/3 * 180/π = -120° cos(-2π/3) = -1/2 sin(-2π/3) = -√3/2 21. 5π/4 5π/4 * 180/π = 225° cos(5π/4) = -√2/2 sin(5π/4) = -√2/2 22. -π/6 -π/6 * 180/π = -30° cos(-π/6) = √3/2 sin(-π/6) = -1/2 Problems 23-26, use each circle to find the length of the indicated arc. Round your answer to the nearest tenth. 23. m = 5(5π/7) m = 25π/7 in m ≈ 11.2 in 24. w = 3(7π/6) w = 21π/6 m w = 7π/2 m w ≈ 11 m 25. b = 2(π/3) b = 2π/3 ft b ≈ 2.1 ft 26. n = 8(3π/4) n = 6π cm n ≈ 18.8 cm Problems 27-30, solve. 27. A pendulum swings through an angle of 2.4 radians. The distance the tip of the pendulum travels is 56 inches. How long is the pendulum? s = rθ 56 = r(2.4) r = 23.3 inches 28. Two arcs have the same length. One arc is intercepted by an angle of 270° in a circle of radius 15 inches. If the radius of the other circle is 25 inches, what is the radian measure of the central angle on the second arc? s₁ = r₁θ₁ s₂ = r₂θ₂ 45π/2 = 25θ₂ θ₂ = 45π/50 = 9π/10 29. There are 24 lines of longitude that are equally spaced around the equator. These lines approximate the standard time zones. A. What is the measure of each angle in degrees and radians? 360°/24 = 15° or 15 * π/180 = π/12 radians B. The radius of the equator is about 3960 miles. Find the width of each time zone at the equator. width = s s = rθ s = 3960 * π/12 s ≈ 1036.7 miles 30. A communication satellite completes a circular orbit around Earth every 2 hours. The radius of Earth is about 6400 km and the satellite orbits 2400 km above Earth's surface. How far does the satellite travel in 1 hour? r = 6400 + 2400 r = 8800 km 1 hr = 180° = π radians s = rθ s = 8800(π) s ≈ 27,646 km