Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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  radians is equal to how many degrees?
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2.
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Which of the following angles, in degrees, is coterminal with, but not equal to,
  radians?
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3.
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Determine the arc length of a circle with radius 5.5 cm if it is subtended by a
central angle of   radians. Round your answer to one
decimal place. A. | 1.4 cm | C. | 4.4 cm | B. | 43.2 cm | D. | 6.9 cm |
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4.
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Determine the measure of the angle in standard position shown on the graph
below. Round your answer to the nearest tenth of a degree. A. | 161.6° | C. | 71.6° | B. | 341.6° | D. | 251.6° |
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5.
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Identify the point on the unit circle corresponding to an angle of  radians in standard position.
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6.
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Which is a possible value of q, to the nearest
hundredth of a radian, when cos q =
–0.58?
A. | –2.19 | C. | 2.19 | B. | –0.62 | D. | 0.84 |
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7.
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During a routine, a figure skater completes  rotations. How many
degrees has the figure skater turned? A. | –400° | C. | –220° | B. | 400° | D. | 580° |
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8.
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If the angle q is 1600° in standard position, in
which quadrant does it terminate?
A. | quadrant III | C. | quadrant II | B. | quadrant IV | D. | quadrant I |
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9.
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A tricycle has a front wheel that is 30 cm in diameter and two rear wheels that
are each 12 cm in diameter. If the front wheel rotates through a angle of 32°, through how many
degrees does each rear wheel rotate, to the nearest tenth of a degree?
A. | 32.0° | C. | 80.0Á | B. | 40.0Á | D. | 160.0Á |
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10.
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Giai got an answer of 3.86 when she was calculating the value of a trigonometric
function. Assuming Giai did her calculation correctly, which of the following was she
calculating?
A. | tan  p | C. | csc  p | B. | sec  p | D. | cot
 p |
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Short Answer
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1.
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A child swings on a playground swing set. If the length of the swing’s
chain is 3 m and the child swings through an angle of  , what is the exact arc length through
which the child travels?
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2.
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Given a circle of diameter 21 cm, determine the arc length
subtended by a central angle of 1.2 radians.
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Problem
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1.
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Sarah and Simone are walking in a walk-a-thon down a straight street that leads
to the finish line in the park. At the same time, they both notice a hot-air balloon directly over
the finish line. Sarah sees the angle from the ground to the balloon as 30° and Simone, who is
0.25 km closer to the finish line than Sarah, sees the angle from the ground to the balloon as
45°.
a) Draw a diagram to represent this situation.
b) If x
represents the distance that Simone is from the finish line, write an expression for the distance
from Sarah to the finish line.
c) Write a trigonometric ratio for each girl’s
position that involves the height of the balloon, h; the distance, x, each girl is away
from the finish line; and the angle from the girl to the balloon.
d) Rearrange each
equation from part c) to isolate h.
e) Set the two expressions for h equal to
each other and solve for x, to the nearest hundredth of a kilometre.
f) Determine
the height of the balloon, to the nearest hundredth of a kilometre.
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2.
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a) Without using a calculator, determine two angles between 0° and
360° that have a sine ratio of  . b) Use a calculator and a diagram to verify your
answers to part a).
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3.
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A bicycle tire revolves at 150 rpm (revolutions per minute). What is its angular
velocity, in radians per second, rounded to two decimal places?
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