Trigonometry Practice Problems – Week 1

Each of the following multiple-choice questions has exactly one correct answer. Click your response to each question.

You may answer the questions in any order. However, once clicked, your response is recorded and scored immediately and cannot be changed.

When all 15 questions have been answered, your score will be automatically calculated and you will be given suggestions for topics to review. These results will appear at the bottom of the problem set.

  1. How many degrees are equal to 3π/8 radians? 

    37.5°
    67.5°
    75°
    135°
  2. Two sides of a right triangle measure 6 cm and 8 cm. Then the third side may be:  

    4 cm
    4√3 cm
    4√7 cm
    12 cm
  3. Which of the following sets of lengths may form a right triangle?  

    28, 45, 53
    30, 30, 9
    5, 13, 14
    18, 18, 18
  4. Which of the following sets of lengths may not form any triangle?  

    6, 15, 22
    1, 12, 12
    45, 65, 85
    53, 57, 59
  5. A piece of gum is stuck to the rim of a 24-inch-diameter bicycle tire. How much distance does the gum travel as the tire rotates through an angle of 4 radians?  

    24/π inches
    24 inches
    24π inches
    48 inches
  6. Choose a valid conclusion from the following hypothesis:

    If two sides of a right triangle have lengths which are even integers,

     

    then the third side must be an even integer as well.
    then the third side must be an odd integer.
    then the third side must be an integer, whether even or odd.
    None of the above.
  7. The angle measuring 1.5 radians is...  

    ...a right angle.
    ...an acute angle.
    ...an obtuse angle.
    ...a straight angle.
  8. For which of the following connections of angles and lengths is exactly one triangle possible?  

    75° — 10 cm — 120°
    45° — 8 cm — 10 cm
    42° — 15 cm — 115°
    30° — 10 cm — 2 cm
  9. If the hypotenuse of a right triangle has length 1, which of the following could be the lengths of the other two sides?  

    0.5 and 0.5
    0.2 and 0.8
    0.6 and 0.8
    0.4375 and 0.75
  10. At 4:00, what angle do the minute and hour hand make on a clock? 

    3π/2 radians
    2π/3 radians
    π/3 radians
    3/(2π) radians
  11. At 4:30, what angle do the minute and hour hand make on a clock? (Careful!) 

    45°
    47.5°
    1 radian
    3π/8 radians
  12. If the bike from #5 is traveling at a speed of 6 meters per second, about how many full revolutions is its 24-inch (about 0.61-meter)-diameter tire making each second?  

    Less than 1
    Between 1 and 2
    Slightly less than 3
    Slightly more than 3
  13. A right triangle has a hypotenuse of 10 cm and an area of 24 cm2. Which of the following can be the length of one of its bases?  

    6 cm
    4 cm
    16 cm
    3 cm
  14. During which minute of the 1:00 hour do the minute and hour hand on a clock overlap?  

    1:05
    1:06
    1:07
    1:08
  15. How many triangles are there whose angles measure 32°, 92°, and 56°? 

    None, because we don't know the lengths.
    None, because the angles don't add up to 360°.
    Infinitely many, because we don't know the lengths.
    Exactly one, because we know all three of the angles exactly.

After you have answered all 15 questions, your results will be displayed here.

Last Modified: September 19, 2011