Question 1

Find the proper coordinates of the point labeled on the given unit circle.
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A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the proper coordinates of the point...

Question 2

Find the proper coordinates of the point labeled on the given unit circle.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the proper coordinates of the point...

Question 3

Find the proper coordinates of the point labeled on the given unit circle.
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A) 
B) 
C) 
D) 23 , - 12

Accepted Answer

The answer of Find the proper coordinates of the point...

Question 4

Solve the problem.
-Two pulleys of diameter 9 m and 3 m are connected by a belt. The larger pulley rotates 39 times per min. Find the angular velocity of the smaller pulley.
A) 117  radians/min
B) 176  radians/min
C) 351  radians/min
D) 234  radians/min

Accepted Answer

The answer of Solve the problem.
-Two pulleys of diameter 9...

Question 5

Find the proper coordinates of the point labeled on the given unit circle.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the proper coordinates of the point...

Question 6

Solve the problem.
-A wheel with a 23-inch diameter is turning at the rate of 47 revolutions per minute. To the nearest inch per minute, what is the velocity of a point on the rim?
A) 3396 in./min
B) 3403 in./min
C) 3442 in./min
D) 3449 in./min

Accepted Answer

The circumference of the wheel is π times the diameter, which is 23 inches. So, the circumference is 23π inches. The velocity is the circumference times the number of revolutions per minute: 23π * 47 ≈ 3396 in./min.

Question 7

Find the exact value of the following expression without using a calculator.
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A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the exact value of the following...

Question 8

Solve the problem.
-A wheel with a 20-inch radius is marked at two points on the rim. The distance between the marks along the wheel is found to be 4 inches. What is the angle (to the nearest tenth of a degree) between the radii to the two
Marks?
A) 7.5°
B) 11.5°
C) 13.5°
D) 9.5°

Accepted Answer

The angle can be found using the arc length formula, $s = r\theta$, where $s$ is the arc length (4 inches), $r$ is the radius (20 inches), and $\theta$ is the angle in radians. Rearranging the formula to solve for $\theta$, we get $\theta = \frac{s}{r}$. Substituting the given values, $\theta = \frac{4}{20} = 0.2$ radians. To convert radians to degrees, we use the conversion factor $\frac{180}{\pi}$, so the angle in degrees is $0.2 \times \frac{180}{\pi} \approx 11.5°$.

Question 9

Solve the problem.
-If a 13-in.-diameter pizza is cut into eight slices of the same size, then what is the area of each piece?
A) 
B) 
C) 
D)

Accepted Answer

The answer of Solve the problem.
-If a 13-in.-diameter pizza is...

Question 10

Solve the problem.
-Find the distance in kilometers between the cities whose latitudes are given. Assume that the cities are on a north-south line and that the radius of the earth is 6400 km. City E, 24°N and city F, 54°S
A) 8713 km
B) 8721 km
C) 3343 km
D) 3351 km

Accepted Answer

The distance between two points on the Earth's surface, given their latitudes and assuming they lie on a north-south line, can be calculated using the formula for arc length, $s = r\theta$, where $s$ is the arc length, $r$ is the radius of the Earth, and $\theta$ is the central angle between the two points in radians. The total latitude difference between City E (24°N) and City F (54°S) is $24° + 54° = 78°$. Converting degrees to radians (since $1° = \frac{\pi}{180}$ radians), we get $78° \times \frac{\pi}{180} = \frac{78\pi}{180} = \frac{13\pi}{30}$ radians. Using the Earth's radius $r = 6400$ km, the distance $s$ is calculated as $s = 6400 \times \frac{13\pi}{30}$. This calculation gives approximately $s \approx 8713$ km, making the correct answer A.

Question 11

Solve the problem.
-Two pulleys of diameter 9 m and 3 m are connected by a belt. The larger pulley rotates 34 times per min. Find the angular velocity of the smaller pulley.
A) 204  radians/min
B) 102  radians/min
C) 153  radians/min
D) 306  radians/min

Accepted Answer

The answer of Solve the problem.
-Two pulleys of diameter 9...

Question 12

Solve the problem.
-A pulley of radius 9 cm rotates 9 times in 128 sec. Find the angular velocity of the pulley.
A) 
B) 
C) 
D)

Accepted Answer

The answer of Solve the problem.
-A pulley of radius 9...

Question 13

Solve the problem.
-Find the distance in kilometers between the cities whose latitudes are given. Assume that the cities are on a north-south line and that the radius of the earth is 6400 km. City A, 18°N and city B, 39°N
A) 2328 km
B) 2403 km
C) 2346 km
D) 2385 km

Accepted Answer

The answer of Solve the problem.
-Find the distance in kilometers...

Question 14

Find the proper coordinates of the point labeled on the given unit circle.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the proper coordinates of the point...

Question 15

Solve the problem.
-A pulley with a diameter of 26 inches is driven by a belt which is moving 876 ft/min. To the nearest unit, how many revolutions per minute are made by the pulley?
A) 234 rpm
B) 227 rpm
C) 141 rpm
D) 129 rpm

Accepted Answer

The answer of Solve the problem.
-A pulley with a diameter...

Question 16

Find the proper coordinates of the point labeled on the given unit circle.
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A) (0, 1)
B) (0, -1)
C) (1, 0)
D) (-1, 0)

Accepted Answer

The answer of Find the proper coordinates of the point...

Question 17

Solve the problem.
-A pulley of radius 5 cm rotates 13 times in 4 sec. Find the angular velocity of the pulley.
A) 
B) 
C) 
D)

Accepted Answer

The answer of Solve the problem.
-A pulley of radius 5...

Question 18

Find the exact value of the following expression without using a calculator.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the exact value of the following...

Question 19

Find the proper coordinates of the point labeled on the given unit circle.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the proper coordinates of the point...

Question 20

Solve the problem.
-A wheel is rotating at 4 radians/sec, and the wheel has a 100-inch diameter. To the nearest foot per minute, what is the velocity of a point on the rim?
A) 990 ft/min
B) 995 ft/min
C) 1005 ft/min
D) 1000 ft/min

Accepted Answer

The velocity $v$ of a point on the rim of a rotating wheel can be found using the formula $v = r\omega$, where $r$ is the radius of the wheel and $\omega$ is the angular velocity in radians per second. Given the diameter of the wheel is 100 inches, the radius $r$ is $50$ inches. Converting the radius to feet, we get $r = \frac{50}{12}$ feet. Given $\omega = 4$ radians/sec, the velocity in feet per second is $v = \frac{50}{12} \times 4$. To convert this to feet per minute, multiply by 60, resulting in $v = \frac{50}{12} \times 4 \times 60 = 1000$ feet per minute.

Quiz 5: The Trigonometric Functions

Find the proper coordinates of the point labeled on the given unit circle. -

Find the proper coordinates of the point labeled on the given unit circle. -

Find the proper coordinates of the point labeled on the given unit circle. -

Solve the problem. -Two pulleys of diameter 9 m and 3 m are connected by a belt. The larger pulley rotates 39 times per min. Find the angular velocity of the smaller pulley.

Find the proper coordinates of the point labeled on the given unit circle. -

Solve the problem. -A wheel with a 23-inch diameter is turning at the rate of 47 revolutions per minute. To the nearest inch per minute, what is the velocity of a point on the rim?

Find the exact value of the following expression without using a calculator. -

Solve the problem. -A wheel with a 20-inch radius is marked at two points on the rim. The distance between the marks along the wheel is found to be 4 inches. What is the angle (to the nearest tenth of a degree) between the radii to the two Marks?

Solve the problem. -If a 13-in.-diameter pizza is cut into eight slices of the same size, then what is the area of each piece?

Solve the problem. -Find the distance in kilometers between the cities whose latitudes are given. Assume that the cities are on a north-south line and that the radius of the earth is 6400 km. City E, 24°N and city F, 54°S

Solve the problem. -Two pulleys of diameter 9 m and 3 m are connected by a belt. The larger pulley rotates 34 times per min. Find the angular velocity of the smaller pulley.

Solve the problem. -A pulley of radius 9 cm rotates 9 times in 128 sec. Find the angular velocity of the pulley.

Solve the problem. -Find the distance in kilometers between the cities whose latitudes are given. Assume that the cities are on a north-south line and that the radius of the earth is 6400 km. City A, 18°N and city B, 39°N

Find the proper coordinates of the point labeled on the given unit circle. -

Solve the problem. -A pulley with a diameter of 26 inches is driven by a belt which is moving 876 ft/min. To the nearest unit, how many revolutions per minute are made by the pulley?

Find the proper coordinates of the point labeled on the given unit circle. -

Solve the problem. -A pulley of radius 5 cm rotates 13 times in 4 sec. Find the angular velocity of the pulley.

Find the exact value of the following expression without using a calculator. -

Find the proper coordinates of the point labeled on the given unit circle. -

Solve the problem. -A wheel is rotating at 4 radians/sec, and the wheel has a 100-inch diameter. To the nearest foot per minute, what is the velocity of a point on the rim?