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Mathematics LibreTexts

5.1e: Exercises - Angles

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    56286
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    A: Concepts

    Exercise \(\PageIndex{A}\) 

    1) Draw an angle in standard position. Label the vertex, initial side, and terminal side.

    2) Explain why there are an infinite number of angles that are coterminal to a certain angle.

    3) State what a positive or negative angle signifies, and explain how to draw each.

    4) How does radian measure of an angle compare to the degree measure? Include an explanation of \(1\) radian in your paragraph.

    Answers to odd exercises:

    1. Graph of a circle with an angle inscribed, showing the initial side, terminal side, and vertex.
    3. Whether the angle is positive or negative determines the direction. A positive angle is drawn in the counterclockwise direction, and a negative angle is drawn in the clockwise direction.

    B: Draw Angles in Standard Position

    Exercise \(\PageIndex{B}\)  

    \( \bigstar \) Draw an angle in standard position with the given measure. If the angle measure is not between \(0\) and \(2 \pi \) or between \(0^{\circ}\) and \(360^{\circ}\), also state the coterminal angle that is within that interval.

    5. \(300^{\circ}\)

    6. \(415^{\circ}\)

    7. \(135^{\circ}\)

    8. \(-30^{\circ}\)

    9. \(-120^{\circ}\)

    10. \(-315^{\circ}\)

    11. \(\dfrac{2π}{3}\)

    12.  \(\dfrac{5π}{3}\)

    13. \(−\dfrac{4π}{3}\)

    14. \(−\dfrac{5π}{3}\)

    15. \(\dfrac{5π}{6}\)

    16.  \(\dfrac{11π}{6}\)

    17. \(−\dfrac{π}{6}\)

    18. \(\dfrac{7π}{6}\)

    19. \( \dfrac{7π}{4}\)

    20. \(\dfrac{5π}{4}\)

    21. \(−\dfrac{3π}{4}\)

    22. \(\dfrac{11π}{4}\)

    23. \(\dfrac{22π}{3}\)

    24. \( \dfrac{17π}{6} \)

    25. \(−\dfrac{π}{10}\)

    26. \(\dfrac{23π}{5}\)

    27. \(\dfrac{π}{2}\)

    28. \( -\dfrac{3π}{2}\)

    29. \( \dfrac{7π}{2}\)

    30. \( -5π \)

    Answers to odd exercises:
    5.  Graph of a circle with an angle inscribed. 7.  Graph of a circle with a 135 degree angle inscribed. 9.   \(240^{\circ}\)Graph of a circle showing the equivalence of two angles. 11.  Graph of a circle with a 2pi/3 radians angle inscribed. 13. \(\frac{2π}{3}\)Graph of a circle showing the equivalence of two angles. x 
    15. 
    Graph of a circle with 5pi/6 radians angle inscribed.  
    17.
    5.1e 17.png
    19.
    5.1 19.png
    21.   
    5.1e 21.png
     
    23. \(\frac{4π}{3}\)
    Graph of a circle showing the equivalence of two angles. 
    25. \(\frac{19π}{10}\) 
    Graph of a circle with a –pi/10 radians angle inscribed. 
      27. 
    5.1e 27.png
    29 .  \(\frac{3π}{2}\)  
    5.1e 29.png
     

    C: Convert between radians and degrees

    Exercise \(\PageIndex{C}\)  

    \( \bigstar \) Convert angles in radians to degrees.

    36. \(\dfrac{3π}{4}\) radians

     

    37. \(\dfrac{π}{9}\) radians

    38. \(−\dfrac{5π}{4}\) radians

     

    39. \(\dfrac{π}{3}\) radians

    40. \(−\dfrac{7π}{3}\) radians

     

    41. \(−\dfrac{5π}{12}\) radians

    42. \(\dfrac{11π}{6}\) radians

     

     

    \( \bigstar \) Convert angles in degrees to radians. Write the answer both as a multiple of pi and to the nearest hundredth of a radian.

    43. \(90^{\circ}\) 44. \(100^{\circ}\) 45. \(-540^{\circ}\) 46. \(-120^{\circ}\) 47. \(180^{\circ}\) 48. \(-315^{\circ}\) 49. \(150^{\circ}\)
    Answers to odd exercises:

    37. \(20^{\circ} \qquad \) 39. \(60^{\circ} \qquad \) 41. \(-75^{\circ} \qquad \) 43. \(\frac{π}{2} \; \approx \; 1.57\) radians  \( \qquad \) 45. \(−3π  \; \approx \; 9.42\) radians
    47. \(π \; \approx \; 3.14 \) radians \( \qquad \) 49. \(\frac{5π}{6} \; \approx \; 2.62\) radians

    D: Coterminal Angles

    Exercise \(\PageIndex{D}\) 

    \( \bigstar \) Find the angle between \(0^{\circ}\) and \(360^{\circ}\) that is coterminal to the given angle.

    50. \(-40^{\circ}\)     \( \qquad \)    51. \(-110^{\circ}\)     \( \qquad \)    52. \(700^{\circ}\)     \( \qquad \)    53. \(1400^{\circ}\)

    \( \bigstar \) Find the angle between \(0\) and \(2\pi \) in radians that is coterminal to the given angle.

    54. \(−\dfrac{π}{9}\)     \( \qquad \)    55. \(\dfrac{10π}{3}\)     \( \qquad \)    56. \(\dfrac{13π}{6}\)     \( \qquad \)    57. \(\dfrac{44π}{9}\)

    Answers to odd exercises:

    51. \(250^{\circ}\)     \( \qquad \)    53. \(320^{\circ}\)     \( \qquad \) 55. \(\frac{4π}{3}\)     \( \qquad \)    57. \(\frac{8π}{9}\)


    5.1e: Exercises - Angles is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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