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Trigonometry

Trigonometry. A brief review . 1.4 Trigonometry. 1.4 Trigonometry. 1.4 Trigonometry. 1.4 Trigonometry. 1.4 Trigonometry. 1.4 Trigonometry. Pythagorean theorem:. 1.4.1. Which one of the following terms is not a trigonometric function? a) cosine b) tangent c) sine

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Trigonometry

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  1. Trigonometry A brief review

  2. 1.4 Trigonometry

  3. 1.4 Trigonometry

  4. 1.4 Trigonometry

  5. 1.4 Trigonometry

  6. 1.4 Trigonometry

  7. 1.4 Trigonometry Pythagorean theorem:

  8. 1.4.1. Which one of the following terms is not a trigonometric function? a) cosine b) tangent c) sine d) hypotenuse e) arc tangent

  9. 1.4.1. Which one of the following terms is not a trigonometric function? a) cosine b) tangent c) sine d) hypotenuse e) arc tangent

  10. 1.4.2. For a given angle , which one of the following is equal to the ratio of sin /cos ? a) one b) zero c) sin1 d) arc cos  e) tan 

  11. 1.4.2. For a given angle , which one of the following is equal to the ratio of sin /cos ? a) one b) zero c) sin1 d) arc cos  e) tan 

  12. 1.4.3. Referring to the triangle with sides labeled A, B, and C as shown, which of the following ratios is equal to the sine of the angle ? • a)

  13. 1.4.3. Referring to the triangle with sides labeled A, B, and C as shown, which of the following ratios is equal to the sine of the angle ? • a)

  14. 1.4.4. Referring to the triangle with sides labeled A, B, and C as shown, which of the following ratios is equal to the tangent of the angle ? • a)

  15. 1.4.4. Referring to the triangle with sides labeled A, B, and C as shown, which of the following ratios is equal to the tangent of the angle ? • a)

  16. 1.4.5. Which law, postulate, or theorem states the following: “The square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.” a) Snell’s law b) Pythagorean theorem c) Square postulate d) Newton’s first law e) Triangle theorem

  17. 1.4.5. Which law, postulate, or theorem states the following: “The square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.” a) Snell’s law b) Pythagorean theorem c) Square postulate d) Newton’s first law e) Triangle theorem

  18. What do you get when you marry measurement and trigonometry Vectors

  19. 1.5 Scalars and Vectors A scalar quantity is one that can be described by a single number: temperature, speed, mass A vector quantity deals inherently with both magnitude and direction: velocity, force, displacement

  20. 1.5 Scalars and Vectors Arrows are used to represent vectors. The direction of the arrow gives the direction of the vector. By convention, the length of a vector arrow is proportional to the magnitude of the vector. 8 lb 4 lb

  21. 1.5 Scalars and Vectors

  22. 1.5.1. Which one of the following statements is true concerning scalar quantities? a) Scalar quantities have both magnitude and direction. b) Scalar quantities must be represented by base units. c) Scalar quantities can be added to vector quantities using rules of trigonometry. d) Scalar quantities can be added to other scalar quantities using rules of ordinary addition. e) Scalar quantities can be added to other scalar quantities using rules of trigonometry.

  23. 1.5.1. Which one of the following statements is true concerning scalar quantities? a) Scalar quantities have both magnitude and direction. b) Scalar quantities must be represented by base units. c) Scalar quantities can be added to vector quantities using rules of trigonometry. d) Scalar quantities can be added to other scalar quantities using rules of ordinary addition. e) Scalar quantities can be added to other scalar quantities using rules of trigonometry.

  24. 1.5.2. Which one of the following quantities is a vector quantity? a) the age of the pyramids in Egypt b) the mass of a watermelon c) the sun's pull on the earth d) the number of people on board an airplane e) the temperature of molten lava

  25. 1.5.2. Which one of the following quantities is a vector quantity? a) the age of the pyramids in Egypt b) the mass of a watermelon c) the sun's pull on the earth d) the number of people on board an airplane e) the temperature of molten lava

  26. 1.5.3. A vector is represented by an arrow. What is the significance of the length of the arrow? a) Long arrows represent velocities and short arrows represent forces. b) The length of the arrow is proportional to the magnitude of the vector. c) Short arrows represent accelerations and long arrows represent velocities. d) The length of the arrow indicates its direction. e) There is no significance to the length of the arrow.

  27. 1.5.3. A vector is represented by an arrow. What is the significance of the length of the arrow? a) Long arrows represent velocities and short arrows represent forces. b) The length of the arrow is proportional to the magnitude of the vector. c) Short arrows represent accelerations and long arrows represent velocities. d) The length of the arrow indicates its direction. e) There is no significance to the length of the arrow.

  28. 1.5.4. Which one of the following situations involves a vector quantity? a) The mass of the Martian soil probe was 250 kg. b) The overnight low temperature in Toronto was 4.0 C. c) The volume of the soft drink can is 0.360 liters. d) The velocity of the rocket was 325 m/s, due east. e) The light took approximately 500 s to travel from the sun to the earth.

  29. 1.5.4. Which one of the following situations involves a vector quantity? a) The mass of the Martian soil probe was 250 kg. b) The overnight low temperature in Toronto was 4.0 C. c) The volume of the soft drink can is 0.360 liters. d) The velocity of the rocket was 325 m/s, due east. e) The light took approximately 500 s to travel from the sun to the earth.

  30. 1.6 Vector Addition and Subtraction Often it is necessary to add one vector to another.

  31. 1.6 Vector Addition and Subtraction 3 m 5 m 8 m

  32. 1.6 Vector Addition and Subtraction

  33. 1.6 Vector Addition and Subtraction 2.00 m 6.00 m

  34. 1.6 Vector Addition and Subtraction R 2.00 m 6.00 m

  35. 1.6 Vector Addition and Subtraction 6.32 m 2.00 m 6.00 m

  36. 1.6 Vector Addition and Subtraction When a vector is multiplied by -1, the magnitude of the vector remains the same, but the direction of the vector is reversed.

  37. 1.6 Vector Addition and Subtraction

  38. 1.6.1. A and B are vectors. Vector A is directed due west and vector B is directed due north. Which of the following choices correctly indicates the directions of vectors A and B? a) A is directed due west and B is directed due north b) A is directed due west and B is directed due south c) A is directed due east and B is directed due south d) A is directed due east and B is directed due north e) A is directed due north and B is directed due west

  39. 1.6.1. A and B are vectors. Vector A is directed due west and vector B is directed due north. Which of the following choices correctly indicates the directions of vectors A and B? a) A is directed due west and B is directed due north b) A is directed due west and B is directed due south c) A is directed due east and B is directed due south d) A is directed due east and B is directed due north e) A is directed due north and B is directed due west

  40. 1.7 The Components of a Vector

  41. 1.7 The Components of a Vector

  42. 1.7 The Components of a Vector It is often easier to work with the scalar components rather than the vector components.

  43. 1.7 The Components of a Vector Example A displacement vector has a magnitude of 175 m and points at an angle of 50.0 degrees relative to the x axis. Find the x and y components of this vector.

  44. 1.7.1. A, B,and, C are three vectors. Vectors B and C when added together equal the vector A. In mathematical form, A = B + C. Which one of the following statements concerning the components of vectors B and C must be true if Ay = 0? a) The y components of vectors B and C are both equal to zero. b) The y components of vectors B and C when added together equal zero. c) ByCy = 0 or CyBy = 0 d) Either answer a or answer b is correct, but never both. e) Either answer a or answer b is correct. It is also possible that both are correct.

  45. 1.7.1. A, B,and, C are three vectors. Vectors B and C when added together equal the vector A. In mathematical form, A = B + C. Which one of the following statements concerning the components of vectors B and C must be true if Ay = 0? a) The y components of vectors B and C are both equal to zero. b) The y components of vectors B and C when added together equal zero. c) ByCy = 0 or CyBy = 0 d) Either answer a or answer b is correct, but never both. e) Either answer a or answer b is correct. It is also possible that both are correct.

  46. 1.7.2. Vector r has a magnitude of 88 km/h and is directed at 25 relative to the x axis. Which of the following choices indicates the horizontal and vertical components of vector r? rxry a) +22 km/h +66 km/h b) +39 km/h +79 km/h c) +79 km/h +39 km/h d) +66 km/h +22 km/h e) +72 km/h +48 km/h

  47. 1.7.2. Vector r has a magnitude of 88 km/h and is directed at 25 relative to the x axis. Which of the following choices indicates the horizontal and vertical components of vector r? rxry a) +22 km/h +66 km/h b) +39 km/h +79 km/h c) +79 km/h +39 km/h d) +66 km/h +22 km/h e) +72 km/h +48 km/h

  48. 1.7.3. A, B,and, C are three vectors. Vectors B and C when added together equal the vector A. Vector A has a magnitude of 88 units and it is directed at an angle of 44 relative to the x axis as shown. Find the scalar components of vectors B and C. BxBy Cx Cy a) 63 0 0 61 b) 0 61 63 0 c) 63 0 61 0 d) 0 63 0 61 e) 61 0 63 0

  49. 1.7.3. A, B,and, C are three vectors. Vectors B and C when added together equal the vector A. Vector A has a magnitude of 88 units and it is directed at an angle of 44 relative to the x axis as shown. Find the scalar components of vectors B and C. BxBy Cx Cy a) 63 0 0 61 b) 0 61 63 0 c) 63 0 61 0 d) 0 63 0 61 e) 61 0 63 0

  50. 1.8 Addition of Vectors by Means of Components

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