Trig Review: 4.1 – 4.2
Short Answer
1. A child swings on a playground swing set. If the length of the swing is 3 m and the child swings through an
angle of
, what is the exact arc length through which the child travels?
2. Darren wishes to cut his birthday cake, which is circular and has a diameter of 30 cm. If his 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?
3. A bicycle tire revolves at 150 rpm (revolutions per minute). What is its angular velocity, in radians per
second, rounded to two decimal places?
4. Determine the exact value of
.
5. 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?
6. In
, XY = 30 cm, YZ = 40 cm, and Y =
. Determine the exact length of the third side.
7. 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
8. If a and b are nonzero constants, simplify
.
9. A 150-cm tall person stands on the bank of a narrow river and observes a flagpole on the opposite bank. If the
angle of elevation to the top of the flagpole is 0.25 and the angle of depression to the bottom of the flagpole is
0.09, determine the flagpole’s height, in metres, to two decimal places.
10. 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 of diameter 6 cm, a height of 10 cm,
and sides that slope outward at an angle of 0.09, determine the cup’s volume.
11. Two billiard balls collide and proceed to separate from one another at the same, constant speed. Assume the
billiard table is frictionless. The angle between the balls is 1.25. After 2 s, the distance between the balls is 1
m. How fast are the balls moving?
ANSWERS
1.
m
2. 0.53 radians
3. 15.71 rad/s
4.
5.
m
6.
cm
7.
8. 3a 2
9. The height of the flagpole is approximately 5.74
m.
10. The volume of the cup is approximately 381 mL.
11. Recall that
.
Therefore, after 2 s, the billiard balls are moving at
approximately 0.43 m/s
SHORT ANSWER
1. ANS:
m
PTS: 1
OBJ: Section 4.1
KEY: arc length
2. ANS:
0.53 radians
DIF: 2
LOC: B1.1
REF: Knowledge and Understanding; Application
TOP: Trigonometric Functions
PTS: 1
DIF: 2
OBJ: Section 4.1
LOC: B1.1
KEY: central angle
3. ANS:
15.71 rad/s
REF: Knowledge and Understanding; Application
TOP: Trigonometric Functions
PTS: 1
DIF: 2
OBJ: Section 4.1
LOC: B1.1
KEY: angular velocity
4. ANS:
REF: Knowledge and Understanding; Application
TOP: Trigonometric Functions
PTS: 1
DIF: 2
REF: Knowledge and Understanding; Application
OBJ: Section 4.2
LOC: B1.4
TOP: Trigonometric Functions
KEY: trigonometric ratios, special angles
5. ANS:
m
PTS: 1
DIF: 2
OBJ: Section 4.2
LOC: B1.4
KEY: special angles
6. ANS:
REF: Knowledge and Understanding; Application
TOP: Trigonometric Functions
cm
PTS: 1
DIF: 4
OBJ: Section 4.2
LOC: B1.4
KEY: special angles
7. ANS:
PTS: 1
OBJ: Section 4.2
KEY: radian
DIF: 2
LOC: B1.2, B1.4
REF: Knowledge and Understanding; Application
TOP: Trigonometric Functions
NOT: law of cosines
REF: Knowledge and Understanding; Application
TOP: Trigonometric Functions
PROBLEM
8. ANS:
PTS: 1
DIF: 3
OBJ: Section 4.2
LOC: B1.4
KEY: special angles
REF: Knowledge and Understanding
TOP: Trigonometric Functions
9. ANS:
Let d represent the width of the river. Let h represent the pole height.
Equate and solve for h.
The height of the flagpole is approximately 5.74 m.
PTS: 1
DIF: 3
REF: Knowledge and Understanding; Thinking; Application
OBJ: Section 4.2
LOC: B1.3
TOP: Trigonometric Functions
KEY: radian, primary trigonometric ratio
10. ANS:
The volume of the cup is approximately 381 mL.
PTS: 1
OBJ: Section 4.2
KEY: volume
DIF: 3
LOC: B1.3
REF: Knowledge and Understanding; Thinking; Application
TOP: Trigonometric Functions
11. ANS:
Recall that
.
Therefore, after 2 s, the billiard balls are moving at
approximately 0.43 m/s.
Use the cosine law.
PTS: 1
DIF: 3
REF: Knowledge and Understanding; Thinking; Application
OBJ: Section 4.2
LOC: B1.3
TOP: Trigonometric Functions
KEY: primary trigonometric ratio, radian