Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Which of the following angles, in degrees, is coterminal with, but not equal to,
  radians?
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2.
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Determine the equation of a circle with centre at the origin and radius
8.
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3.
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Which graph represents an angle in standard position with a measure of  p rad?
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4.
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Which graph represents an angle in standard position with a measure of
135°?
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5.
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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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6.
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John cuts a slice from a circular ice cream cake with a diameter of 24 cm. His
slice is in the shape of a sector with an arc length of 7 cm. What is the measure of the central
angle of the slice, in radians? Round your answer to two decimal places, if necessary.
A. | 1.71 rad | C. | 0.29 rad | B. | 3.43 rad | D. | 0.58 rad |
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7.
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A ball is riding the waves at a beach. The ball’s up and down motion with
the waves can be described using the formula  , where h is the height, in metres,
above the flat surface of the water and t is the time, in seconds. What is the height of the
ball, to the nearest hundredth of a metre, after t = 17 s? A. | –0.87 m | C. | –1.99 m | B. | –2.66 m | D. | 1.99 m |
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8.
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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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9.
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The point P(0.391, 0.921) is the point of intersection of a unit circle and the
terminal arm of an angle q in standard position. What is the equation of
the line passing through the centre of the circle and the point P? Round the slope to two decimal
places.
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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
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Short Answer
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1.
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Determine the exact value of  .
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2.
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Given that  and that x lies in the first quadrant, determine the
exact measure of angle x.
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Problem
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1.
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Adriano knows that the distance from the point on the bridge where he is
standing to one side of the canyon floor is 725 m, and that the distance from where he is to a point
on the other side of the canyon floor is 816 m. If Adriano measures the angle between the two points
on the canyon floor to be 11°, determine the width of the canyon, to the nearest tenth of a
metre.
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2.
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a) For the given trigonometric ratio, determine two other angles that
have the same value.
i) sin 45°
ii) tan 300°
iii) cos
120°
b) Explain how you determined the angles in part a).
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3.
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A group of marketing students are creating a strategy to
sell ceiling fans. They determine that the number of sales will vary according to the month of the
year. The formula  gives the expected sales, in thousands, according to the
month, t, where t = 1 represents January, t = 2 is February, and so
on.
a) In which month are sales of fans expected to reach 11 600?
b) In which
month are sales expected to be the least?
c) Does this formula seem reasonable?
Explain.
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