Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Solve the equation for exact
solutions over the interval [0, 2ð). cos2x + 2
cos x + 1 = 0
a. |  | c. | {2ð} | b. |  | d. | {ð} |
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2.
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Solve the equation for exact
solutions over the interval [0, 2ð). 2 sin2x =
sin x
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3.
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Solve the equation for exact
solutions over the interval [0, 2ð). cos x =
sin x
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4.
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Solve the equation for exact
solutions over the interval [0, 2ð). sec2x - 2
= tan2x
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5.
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Solve the equation for exact
solutions over the interval [0, 2ð). tan x +
sec x = 1
a. |  | c. | {0} | b. | Ø | d. |  |
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6.
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Solve the equation for exact
solutions over the interval [0, 2ð). csc5x - 4
csc x = 0
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7.
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Solve the equation for exact
solutions over the interval [0, 2ð). sin2x +
sin x = 0
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8.
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Solve the equation in the
interval [0°, 360°). Give solutions to the nearest tenth, if necessary.
csc
è = 1 + cot è
a. | Ø | c. | {90°, 270°} | b. | {90°} | d. | {270°} |
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9.
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Solve the equation in the
interval [0°, 360°). Give solutions to the nearest tenth, if necessary.
2
cos3è = cos è
a. | Ø | c. | {90°, 270°} | b. | {45°, 90°, 135°, 225°, 270°,
315°} | d. | {45°, 135°, 225°,
315°} |
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10.
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Solve the equation in the
interval [0°, 360°). Give solutions to the nearest tenth, if necessary.
sin
2è = -sin è
a. | {60°, 120°, 240°,
300°} | c. | {0°,
60°, 120°, 180°, 240°, 300°} | b. | {0°, 120°, 180°,
240°} | d. | {0°,
180°} |
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11.
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Solve the equation in the
interval [0°, 360°). Give solutions to the nearest tenth, if necessary.
2
cos2è + 7 sin è =
5
a. | {90°, 48.6°,
131.4°} | c. | Ø | b. | {30°, 210°} | d. | {30°, 330°} |
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12.
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Solve the equation (x in
radians and è in degrees) for all exact solutions where
appropriate. Round approximate answers in radians to four decimal places and approximate answers in
degrees to the nearest tenth.
4  x - 1 = 0
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13.
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Solve the equation (x in
radians and è in degrees) for all exact solutions where
appropriate. Round approximate answers in radians to four decimal places and approximate answers in
degrees to the nearest tenth.
 x - cos x = 0
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14.
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Solve the equation (x in
radians and è in degrees) for all exact solutions where
appropriate. Round approximate answers in radians to four decimal places and approximate answers in
degrees to the nearest tenth.
2  x + sin x = 1
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15.
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Solve the equation (x in
radians and è in degrees) for all exact solutions where
appropriate. Round approximate answers in radians to four decimal places and approximate answers in
degrees to the nearest tenth.
3 cos2è + 2 cos
è = 1
a. | {70.5° + 360°n, 180°
+ 360°n, 289.5° + 360°n} | b. | {51.8° + 360°n, 128.2° +
360°n} | c. | {103.2° + 360°n, 145.2° + 360°n, 283.2° + 360°n,
325.2° + 360°n} | d. | {49.8° + 360°n, 130.2° + 360°n, 229.8° + 360°n,
310.2° + 360°n} |
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16.
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Solve the equation (x in
radians and è in degrees) for all exact solutions where
appropriate. Round approximate answers in radians to four decimal places and approximate answers in
degrees to the nearest tenth.
 = 1
a. | {0° + 180°n,
45° + 180°n, 101.3° + 180°n} | c. | { 45° + 180°n, 101.3° +
180°n} | b. | Ø | d. | { 45° + 360°n,
101.3° + 360°n} |
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17.
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A generator produces an
alternating current according to the equation  where t is time in seconds
and I is the current in amperes. What is the smallest time t such that 
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18.
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The area of a triangle is given
by
A =  ab sin C,
where a and b are the lengths of
two of the sides and C is the included angle. If    and C is an acute angle, what must C be? Give your answer in degrees to the nearest
hundredth.
a. | 53.66° | c. | 126.34° | b. | 26.83° | d. | No such triangle exists. |
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19.
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The position of a weight on a
spring relative to the point of equilibrium is given by
y = 4 cos 6t - 2
sin 6t,
where the arguments are in radians and t is in seconds. Find the smallest value of t
for which the weight is at the point of equilibrium  Give your answer to the
nearest hundredth.
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20.
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Snell's Law states
that
 =  ,
where  ,
 are the speeds at which light travels through
two different mediums, and  ,  are the angles of incidence
and refraction respectively. Find the angle of refraction if  and the
angle of incidence is 26°. Give your answer in degrees to the nearest
hundredth.
a. | 5.24° | c. | 7.87° | b. | 44.54° | d. | 15.90° |
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21.
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It can be shown that if the
angle of elevation from an observer to the top of an object is A and the angle of elevation d ft
closer is B, then the height of the object is given by
h =  ft.
Find
A if   and 
Give your answer in degrees to the nearest hundredth.
a. | 39.97° | c. | 55.72° | b. | 46.34° | d. | 51.51° |
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22.
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Let (a, b) and (c, d) be two
points in the first quadrant, and let è be the angle between the line
segment connecting (a, b) with the origin and the line segment connecting (c, d) with the origin. It
can be shown that
cos è =  .
Find
è if    and  Give your answer in degrees rounded to the nearest hundredth.
a. | 78.62° | c. | 40.43° | b. | 55.68° | d. | 111.50° |
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