Math 3200 Unit 4 Review Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. 4 3 radians is equal to how many degrees? A. 240° C. 420° B. 150° D. 330° ____ 2. The exact radian measure for an angle of 255° is A. 17 12 C. 17 6 B. 12 17 D. 6 17 ____ 3. Which of the following angles, in degrees, is coterminal with, but not equal to, 6 5 radians? A. 396° C. 486° B. 576° D. 216° ____ 4. Determine the arc length of a circle with radius 5.5 cm if it is subtended by a central angle of 5 2 radians. Round your answer to one decimal place. A. 1.4 cm C. 4.4 cm B. 43.2 cm D. 6.9 cm ____ 5. Determine the equation of a circle with centre at the origin and radius 8. A. C. B. D. ____ 6. Determine the equation of a circle with centre at (3, –3) and radius 10. A. C. B. D. ____ 7. Which graph represents an angle in standard position with a measure of 5 8 rad? A. x y C. x y
Transcript
Math 3200 Unit 4 Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. 4
3 radians is equal to how many degrees?
A. 240° C. 420°
B. 150° D. 330°
____ 2. The exact radian measure for an angle of 255° is
A. 17
12
C. 17
6
B. 12
17
D. 6
17
____ 3. Which of the following angles, in degrees, is coterminal with, but not equal to, 6
5 radians?
A. 396° C. 486°
B. 576° D. 216°
____ 4. Determine the arc length of a circle with radius 5.5 cm if it is subtended by a central angle of 5
2 radians.
Round your answer to one decimal place.
A. 1.4 cm C. 4.4 cm
B. 43.2 cm D. 6.9 cm
____ 5. Determine the equation of a circle with centre at the origin and radius 8.
A. C.
B. D.
____ 6. Determine the equation of a circle with centre at (3, –3) and radius 10.
A. C.
B. D.
____ 7. Which graph represents an angle in standard position with a measure of 5
8 rad?
A.
x
y C.
x
y
B.
x
y D.
x
y
____ 8. Which graph represents an angle in standard position with a measure of 135°?
A.
x
y C.
x
y
B.
x
y D.
x
y
____ 9. Determine the measure of the angle in standard position shown on the graph below. Round your answer to the
nearest tenth of a degree.
(1, 3)
x
y
A. 161.6° C. 71.6°
B. 341.6° D. 251.6°
____ 10. 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
____ 11. 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)
____ 12. Identify the point on the unit circle corresponding to an angle of 300° in standard position.
A. ( , )
C. ( , )
B. ( , )
D. ( , )
____ 13. Identify the point on the unit circle corresponding to an angle of radians in standard position.
A. ( , )
C. ( , )
B. ( , )
D. ( , )
____ 14. Which point on the unit circle corresponds to tan = ?
A. ( , )
C. ( , )
B. ( , )
D. ( , )
____ 15. Identify a measure for the central angle in the interval such that point ( ) is on the
terminal arm.
A. C.
B.
D.
____ 16. Which is a possible value of to the nearest hundredth of a radian, when cos –0.58?
A. –2.19 C. 2.19
B. –0.62 D. 0.84
____ 17. If the angle is –5000° in standard position, it can be described as having made
A. 13
8
9 rotations
C. 27
7
9 rotations
B. 13
8
9 rotations
D. 27
7
9 rotations
____ 18. During a routine, a figure skater completes 11
9 rotations. How many degrees has the figure skater turned?
A. –400° C. –220°
B. 400° D. 580°
____ 19. If the angle is 1600° in standard position, in which quadrant does it terminate?
A. quadrant III C. quadrant II
B. quadrant IV D. quadrant I
____ 20. 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
____ 21. 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. 80.0
B. 40.0 D. 160.0
____ 22. Determine the point in quadrant II where the line represented by intersects the unit circle.
A. (0.95, –0.32) C. (–0.35, 0.94)
B. (–0.32, 0.95) D. (–0.32, 0.94)
____ 23. The point P(0.391, 0.921) is the point of intersection of a unit circle and the terminal arm of an angle 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.
A. C.
B. D.
____ 24. 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
1
12
C. csc
1
12
B. sec
7
12
D. cot
1
12
____ 25. A bottle is riding the waves at a beach. The bottle’s up and down motion with the waves can be described
using the formula , where h is the height, in metres, above the flat water surface and t is the
time, in seconds. When is the first time, to the nearest tenth of a second, that the height of the bottle will be
1.4 m?
A. 14.8 s C. 0.9 s
B. 1.1 s D. 1.5 s
Short Answer
1. 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?
2. Determine the exact value of .
3. A 3-m ladder is leaning against a vertical wall such that the angle between the ground and the ladder is .
What is the exact height that the ladder reaches up the wall?
4. Find the exact value of .
5. Find the exact value of .
6. Given that and that x lies in the first quadrant, determine the exact measure of angle x.
7. Find the exact value of .
8. Angles A and B are located in the first quadrant. If and , determine the exact
value of sec A + sec B.
9. Determine the exact measures for all angles where in the domain .
10. 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?
Problem
1. The volume of a drinking cup can be approximated by the formula , where the top and
bottom of the cup are circular and h is the height. If the cup has a bottom diameter of 6 cm, a height of 10 cm,
and sides that slope outward at an angle of 0.09, determine the cup’s volume.
2. Two billiard balls collide and then separate from one another at the same, constant speed. Assume the billiard
table is frictionless. The angle between the balls is 1.25 radians. After 2 s, the distance between the balls is 1
m. How fast are the balls moving, to the nearest hundredth of a metre per second?
3. Gursant and Leo are both standing on the north side of a monument that is 6.0 m tall. Leo is standing 3.5 m
closer to the monument than Gursant. Leo measures the angle from the ground to the top of the monument to
be 41°. Determine the angle that Gursant would measure from the ground to the top of the monument, to the
nearest degree.
4. The point (–5, 7) is located on the terminal arm of A in standard position.
a) Determine the primary trigonometric ratios for A.
b) Determine the primary trigonometric ratios for B with the same sine as A, but different signs for the
other two primary trigonometric ratios.
c) Use a calculator to determine the measures of A and B, to the nearest degree.
5. 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).
6. Jason is standing 8.7 km from town X and 11.5 km from town Y. From where he stands, the angle between
the two towns is 37°. A new hotel has just been built on the road connecting town X and town Y, exactly
halfway between the two towns. From where Jason is standing, he sees that the angle of elevation to the top of
the hotel is 1°. Determine the height of the hotel, to the nearest tenth of a metre. Include a diagram with your
solution.
7. A rectangle has a diagonal of 8 cm. The diagonal creates a 60° angle at the base of the rectangle.
a) Write an exact expression for the base and the height of the rectangle.
b) Use your expressions to find the exact area of the rectangle.
8. 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.
9. Darren cuts a slice from his circular birthday cake, which has a diameter of 30 cm. The slice is in the shape of
a sector with arc length 8 cm. What is the measure of the central angle of the slice, in radians, rounded to two
decimal places?
10. A bicycle tire revolves at 150 rpm (revolutions per minute). What is its angular velocity, in radians per
