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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Determine the equation of a circle with centre at (3, –3) and radius
10.
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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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Identify a measure for the central angle q in the
interval  such that point (  ,  ) is on the terminal arm.
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7.
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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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8.
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Which function is represented by the graph shown below, where x is in
degrees? A. | y = sin( x) | C. | y = cos( x) | B. | y =
cos(x) | D. | y
= sin(x) |
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9.
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What is the amplitude of the sinusoidal function  ? A. |  | C. | –5 | B. | –8 | D. | 7 |
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10.
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Which graph represents the sinusoidal function  ?
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11.
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What are the solutions for   = 0 in the interval  ? A. |     | C. | x = 90° and 270°  | B. | x = 30° and 210°  | D. | x = 60°
and 240° and 45°
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Use the following information to answer the questions.The height,
h, in centimetres, of a piston moving up and down in an engine cylinder can be modelled by the
function  , where t is the time, in seconds.
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12.
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What is the piston’s minimum height?
A. | 14 cm | C. | 0 cm | B. | –14 cm | D. | 7 cm |
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13.
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Solve  , to the nearest tenth of a degree, if necessary, on the
interval  . A. | x = 53.1°, x = 126.9° | C. | x = 36.9°, x =
323.1° | B. | x = 126.9°, x = 233.1° | D. | x = 53.1°, x = 306.9° |
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14.
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What is an equivalent expression for  ?
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15.
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Express  in terms of cosine and sine only, and simplify. A. | 0 | C. | 1 | B. |  | D. |  |
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16.
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Simplify  . Round your answer to the nearest hundredth. A. | 0.47 | C. | –0.75 | B. | –1.15 | D. | 0.42 |
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17.
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Which expression is equivalent to  ?
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18.
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What is the solution to the equation  over the domain  ?
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19.
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What is the general solution, in degress, to the equation  ?
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20.
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What is the general solution, in radians, to the equation  ? A. |  , where  | C. | no solution | B. |  , where  | D. |  , where  |
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Short Answer
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1.
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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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2.
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Angles A and B are located in the first quadrant. If  and  , determine the exact value of sec A + sec B.
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3.
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A grandfather clock shows a time of 7 o’clock. What is the exact radian
measure of the angle between the hour hand and the minute hand?
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4.
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Sketch the graph of  for two cycles and state the domain, range, period, and
equations of the asymptotes. x is measured in radians.
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5.
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Find the exact value of  .
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Problem
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1.
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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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2.
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Sketch the graph of  for  .
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3.
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Prove the identity  .
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