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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The exact radian measure for an angle of 255° is
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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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The coordinates of the point that lies at the intersection of the terminal arm
and the unit circle at an angle of 110° are
A. | (0.94, –0.34) | C. | (–0.34, 0.94) | B. | (–0.34, –2.75) | D. | (–2.75,
0.94) |
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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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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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7.
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Which function is represented by the graph shown below, where q is in radians?
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8.
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What is the amplitude of the sinusoidal function  ? A. |  | C. | –5 | B. | –8 | D. | 7 |
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9.
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What is the period of the sinusoidal function  ?
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10.
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Which graph represents the sinusoidal function  ?
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11.
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Give an equation for a transformed sine function with an amplitude of  , a
period of  , a phase shift of  rad to the right, and a vertical translation of 9 units
down.
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12.
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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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13.
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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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14.
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What is the period?
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15.
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Which equation is a reciprocal identity?
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16.
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What is an equivalent expression for  ?
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17.
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Which expression is equivalent to  ?
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18.
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Which expression is equivalent to  ?
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19.
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Which expression is equivalent to  ?
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20.
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Simplify  .
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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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Solve  on the interval  .
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3.
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A pebble is embedded in the tread of a rotating bicycle wheel of diameter 60 cm.
If the wheel rotates at 4 revolutions per second, determine a relationship between the height,
h, in centimetres, of the pebble above the ground as a function of time, t, in
seconds.
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4.
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Determine the value of  if  and  .
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5.
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Use a counterexample to show that  is not an identity.
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Problem
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1.
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Prove the identity  .
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2.
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Prove the identity  .
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3.
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Solve  over the domain  .
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