Question 1

$$\text { Convert the degree measure to radians, correct to four decimal places. Use } 3.1416 \text { for } \pi \text {. }$$
-351°10´
A)6.109
B)6.099
C)6.129
D)6.119

Accepted Answer

The answer of \[\text { Convert the degree measure to...

Question 2

$$\text { Find the value of s in the interval } [ 0 , \pi / 2 ] \text { that makes the statement true. Round to four decimal places. }$$
-cot s = 0.6921
A)0.3178
B)0.9654
C)0.7470
D)4.1070

Accepted Answer

The answer of \[\text { Find the value of s...

Question 3

The figure shows an angle in standard position with its terminal side intersecting the unit circle. Evaluate the indicated
circular function value of .
-$$\text { Find } \tan \theta \text {. }$$

A) $-\frac{24}{7}$
B) $-\frac{25}{7}$
C) $-\frac{7}{24}$
D) $\frac{25}{24}$

Accepted Answer

The answer of The figure shows an angle in standard...

Question 4

The figure shows an angle in standard position with its terminal side intersecting the unit circle. Evaluate the indicated
circular function value of .
-Find $\cos \theta$.

A) $- \frac { 5 } { 12 }$
B) $- \frac { 12 } { 13 }$
C) $\frac { 12 } { 13 }$
D) $- \frac { 5 } { 13 }$

Accepted Answer

The answer of The figure shows an angle in standard...

Question 5

Find the exact circular function value.
-$$\sec \frac { 3 \pi } { 4 }$$
A) $\frac { \sqrt { 2 } } { 2 }$
B) $- \frac { 2 \sqrt { 3 } } { 3 }$
C) $- 2$
D) $- \sqrt { 2 }$

Accepted Answer

The secant function is the reciprocal of the cosine function. For $\frac{3\pi}{4}$, the cosine value is $-\frac{\sqrt{2}}{2}$. Therefore, the secant value, being the reciprocal, is $-\sqrt{2}$.

Question 6

Solve the problem.
-A pendulum swings through an angle of $18 ^ { \circ }$ each second. If the pendulum is $20 \mathrm {~cm}$ in length and the complete swing from right to left lasts 2 seconds, what area is covered by each complete swing? Round to the nearest hundredth.
A) $62.83 \mathrm {~cm} ^ { 2 }$
B) $6.28 \mathrm {~cm} ^ { 2 }$
C) $251.33 \mathrm {~cm} ^ { 2 }$
D) $125.66 \mathrm {~cm} ^ { 2 }$

Accepted Answer

The pendulum swings through a total angle of $36^\circ$ in a complete swing (right to left and back). The area covered by the swing is a sector of a circle with radius $20 \mathrm{~cm}$ and angle $36^\circ$. The area of the sector is $\frac{36}{360} \times \pi \times (20)^2 = 125.66 \mathrm{~cm}^2$.

Question 7

Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π.
-72°
A)1.0566
B)1.1566
C)0.9566
D)1.2566

Accepted Answer

The answer of Convert the degree measure to radians, correct...

Question 8

Find the value of s in the interval [0, π/2] that makes the statement true. Round to four decimal places.
-sin s = 0.5954
A)-0.4962
B)0.6378
C)0.6454
D)2.5038

Accepted Answer

The value of s that makes sin s = 0.5954 in the interval [0, π/2] can be found using the inverse sine function (sin^-1 or arcsin). Using a calculator, arcsin(0.5954) ≈ 0.6378.

Question 9

Solve the problem.
-The minute hand of a clock is 13 inches long. What distance does its tip move in 16 minutes? Give an exact answer. 
A) $\frac { 104 } { 15 } \pi \mathrm { in }$.
B) $\frac { 4 } { 195 } \pi$ in.
C) $\frac { 8 } { 195 } \pi \mathrm { in }$.
D) $\frac { 52 } { 15 } \pi \mathrm { in }$.

Accepted Answer

The distance covered by the tip of the minute hand in 16 minutes can be calculated using the formula for the circumference of a circle, $C = 2\pi r$, where $r$ is the radius (length of the minute hand). Since the minute hand completes one full circle in 60 minutes, in 16 minutes, it covers $\frac{16}{60}$ of the full circle. Thus, the distance is $2\pi(13) \times \frac{16}{60} = \frac{104}{15}\pi$ inches.

Question 10

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km.
-Find the latitude of Spokane, WA if Spokane and Jordan Valley, OR, 43.15° N, are 486 km apart.
A)38.8 °N
B)39.5 °N
C)47.5 °N
D)52.46 °N

Accepted Answer

The latitude difference between two locations on the same meridian (north-south line) can be calculated by dividing the distance between them by the Earth's circumference (assuming a spherical Earth) and then converting the result into degrees. The Earth's circumference is approximately 2πr, where r is the radius of the Earth. Given r = 6400 km, the circumference is about 2 * π * 6400 = 40,212 km. The distance between Spokane and Jordan Valley is 486 km. The fraction of the Earth's circumference this distance represents is 486 / 40,212. To convert this fraction into degrees, we multiply by 360 (since a full circle is 360 degrees). Thus, the latitude difference is (486 / 40,212) * 360. This calculation gives approximately 4.35 degrees. Since Jordan Valley is at 43.15° N and Spokane is north of Jordan Valley, we add this difference to Jordan Valley's latitude to find Spokane's latitude: 43.15 + 4.35 ≈ 47.5° N.

Question 11

$$\text { Find the value of s in the interval } [ 0 , \pi / 2 ] \text { that makes the statement true. Round to four decimal places. }$$
-tan s = 7.6725
A)1.4412
B)0.8420
C)1.0120
D)4.5828

Accepted Answer

To find the value of $s$ given $\tan(s) = 7.6725$, we use the inverse tangent function: $s = \tan^{-1}(7.6725)$. Calculating this value gives us $s \approx 1.4412$, which is in the interval $[0, \pi/2]$.

Question 12

Find the exact circular function value.
-$\csc \frac { - 2 \pi } { 3 }$
A) $- \frac { 2 \sqrt { 3 } } { 3 }$
B) $- \frac { 1 } { 2 }$
C) $- \sqrt { 2 }$
D) $- \sqrt { 3 }$

Accepted Answer

The answer of Find the exact circular function value.
-\(\csc \frac...

Question 13

Solve the problem.
-A circular pulley is rotating about its center. Through how many radians would it turn in 22 r 
A) $66 \pi$
B) $110 \pi$
C) $88 \pi$
D) $44 \pi$ otations?

Accepted Answer

One full rotation of a circle is $2\pi$ radians. Therefore, for 22 rotations, the pulley would turn $22 \times 2\pi = 44\pi$ radians.

Question 14

Find the exact value without using a calculator.
-$$\sec \frac { 3 \pi } { 4 }$$
A) $\frac { \sqrt { 2 } } { 2 }$
B) $- \sqrt { 2 }$
C) $- 2$
D) $- \frac { 2 \sqrt { 3 } } { 3 }$

Accepted Answer

The secant function is the reciprocal of the cosine function. $\sec \frac { 3 \pi } { 4 } = \frac{1}{\cos \frac { 3 \pi } { 4 }}$. The cosine of $\frac { 3 \pi } { 4 }$ is $-\frac{\sqrt{2}}{2}$, so its reciprocal is $-\sqrt{2}$.

Question 15

Find the exact values of s in the given interval that satisfy the given condition.
-$$[ 0,2 \pi ) ; \sin s = \frac { \sqrt { 3 } } { 2 }$$
A) $\frac { \pi } { 3 }$
B) $\frac { \pi } { 4 } , \frac { 3 \pi } { 4 }$
C) $\frac { \pi } { 4 }$
D) $\frac { \pi } { 3 } , \frac { 2 \pi } { 3 }$

Accepted Answer

The sine function equals $\frac{\sqrt{3}}{2}$ at angles $\frac{\pi}{3}$ and $\frac{2\pi}{3}$ within the interval $[0, 2\pi)$.

Question 16

The figure shows an angle in standard position with its terminal side intersecting the unit circle. Evaluate the indicated
circular function value of .
-Find $\sec \theta$.

A) $\frac { 12 } { 5 }$
B) $\frac { 13 } { 5 }$
C) $- \frac { 13 } { 5 }$
D) $- \frac { 5 } { 13 }$

Accepted Answer

The answer of The figure shows an angle in standard...

Question 17

Convert the radian measure to degrees. Round to the nearest hundredth if necessary.
-$- 13 \pi$
A) $- 2520 ^ { \circ }$
B) $- 4680 ^ { \circ }$
C) $- 1170 ^ { \circ }$
D) $- 2340 ^ { \circ }$

Accepted Answer

To convert radians to degrees, multiply by $\frac{180}{\pi}$. So, $-13\pi \times \frac{180}{\pi} = -2340^\circ$.

Question 18

Solve the problem.
-Suppose the tip of the minute hand of a clock is 6 inches from the center of the clock. Determine the distance traveled by the tip of the minute hand in 30 minutes. Give an exact answer. 
A) $6 \pi \mathrm { in }$.
B) $3 \pi \mathrm { in }$.
C) $12 \pi \mathrm { in }$.
D) $36 \pi \mathrm { in }$.

Accepted Answer

The distance traveled by the tip of the minute hand in 30 minutes is half the circumference of the circle it describes. The circumference of a circle is given by $C = 2\pi r$, where $r$ is the radius. Here, $r = 6$ inches, so $C = 2\pi(6) = 12\pi$ inches for the full hour. For 30 minutes, which is half the circle, the distance is $12\pi / 2 = 6\pi$ inches.

Question 19

Convert the radian measure to degrees. Round to the nearest hundredth if necessary.
-$$- \frac { \pi } { 4 }$$
A) $- 0.79 ^ { \circ }$
B) $- \frac { \pi } { 4 }$ 。
C) $- 45 ^ { \circ }$
D) $- 45 \pi ^ { \circ }$

Accepted Answer

To convert radians to degrees, use the conversion factor $180^\circ/\pi$. Thus, $-\frac{\pi}{4}$ radians equals $-\frac{\pi}{4} \times \frac{180^\circ}{\pi} = -45^\circ$.

Question 20

Solve the problem.
-Electrical wire is being wound around a drum with radius of 1.49 meters. How much line (to the nearest hundredth of a meter)would be wound around the drum if it is rotated through an angle of
275.3°?
A)7.16 m
B)7.26 m
C)6.96 m
D)7.06 m

Accepted Answer

The length of the line wound around the drum can be found using the formula for the arc length, $s = r\theta$, where $s$ is the arc length, $r$ is the radius, and $\theta$ is the angle in radians. First, convert the angle from degrees to radians: $275.3° \times \frac{\pi}{180°} = 4.804$ radians. Then, calculate the arc length: $s = 1.49 \times 4.804 = 7.15796$ meters, which rounds to $7.16$ meters to the nearest hundredth.

Quiz 3: Radian Measure and the Unit Circle

$\text { Convert the degree measure to radians, correct to four decimal places. Use } 3.1416 \text { for } \pi \text {. }$ -351°10´

$\text { Find the value of s in the interval } [ 0 , \pi / 2 ] \text { that makes the statement true. Round to four decimal places. }$ -cot s = 0.6921

Find the exact circular function value. - $\sec \frac { 3 \pi } { 4 }$

Solve the problem. -A pendulum swings through an angle of $18 ^ { \circ }$ each second. If the pendulum is $20 \mathrm {~cm}$ in length and the complete swing from right to left lasts 2 seconds, what area is covered by each complete swing? Round to the nearest hundredth.

Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π. -72°

Find the value of s in the interval [0, π/2] that makes the statement true. Round to four decimal places. -sin s = 0.5954

Solve the problem. -The minute hand of a clock is 13 inches long. What distance does its tip move in 16 minutes? Give an exact answer.

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km. -Find the latitude of Spokane, WA if Spokane and Jordan Valley, OR, 43.15° N, are 486 km apart.

$\text { Find the value of s in the interval } [ 0 , \pi / 2 ] \text { that makes the statement true. Round to four decimal places. }$ -tan s = 7.6725

Find the exact circular function value. - $\csc \frac { - 2 \pi } { 3 }$

Solve the problem. -A circular pulley is rotating about its center. Through how many radians would it turn in 22 r

Find the exact value without using a calculator. - $\sec \frac { 3 \pi } { 4 }$

Find the exact values of s in the given interval that satisfy the given condition. - $[ 0,2 \pi ) ; \sin s = \frac { \sqrt { 3 } } { 2 }$

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - $- 13 \pi$

Solve the problem. -Suppose the tip of the minute hand of a clock is 6 inches from the center of the clock. Determine the distance traveled by the tip of the minute hand in 30 minutes. Give an exact answer.

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - $- \frac { \pi } { 4 }$

Solve the problem. -Electrical wire is being wound around a drum with radius of 1.49 meters. How much line (to the nearest hundredth of a meter) would be wound around the drum if it is rotated through an angle of 275.3°?

Quiz 3: Radian Measure and the Unit Circle

The figure shows an angle in standard position with its terminal side intersecting the unit circle. Evaluate the indicated circular function value of . - Find tan⁡θ. \text { Find } \tan \theta \text {. } Find tanθ.

The figure shows an angle in standard position with its terminal side intersecting the unit circle. Evaluate the indicated circular function value of . -Find cos⁡θ\cos \thetacosθ .

Find the exact circular function value. - sec⁡3π4\sec \frac { 3 \pi } { 4 }sec43π​

Solve the problem. -A pendulum swings through an angle of 18∘18 ^ { \circ }18∘ each second. If the pendulum is 20 cm20 \mathrm {~cm}20 cm in length and the complete swing from right to left lasts 2 seconds, what area is covered by each complete swing? Round to the nearest hundredth.

Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π. -72°

Find the value of s in the interval [0, π/2] that makes the statement true. Round to four decimal places. -sin s = 0.5954

Solve the problem. -The minute hand of a clock is 13 inches long. What distance does its tip move in 16 minutes? Give an exact answer.

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km. -Find the latitude of Spokane, WA if Spokane and Jordan Valley, OR, 43.15° N, are 486 km apart.

Find the exact circular function value. - csc⁡−2π3\csc \frac { - 2 \pi } { 3 }csc3−2π​

Solve the problem. -A circular pulley is rotating about its center. Through how many radians would it turn in 22 r

Find the exact value without using a calculator. - sec⁡3π4\sec \frac { 3 \pi } { 4 }sec43π​

Find the exact values of s in the given interval that satisfy the given condition. - [0,2π) ;sin⁡s=32[ 0,2 \pi ) ; \sin s = \frac { \sqrt { 3 } } { 2 }[0,2π) ;sins=23​​

The figure shows an angle in standard position with its terminal side intersecting the unit circle. Evaluate the indicated circular function value of . -Find sec⁡θ\sec \thetasecθ .

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - −13π- 13 \pi−13π

Solve the problem. -Suppose the tip of the minute hand of a clock is 6 inches from the center of the clock. Determine the distance traveled by the tip of the minute hand in 30 minutes. Give an exact answer.

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - −π4- \frac { \pi } { 4 }−4π​

Solve the problem. -Electrical wire is being wound around a drum with radius of 1.49 meters. How much line (to the nearest hundredth of a meter) would be wound around the drum if it is rotated through an angle of 275.3°?

Find the exact circular function value. - $\sec \frac { 3 \pi } { 4 }$

Solve the problem. -A pendulum swings through an angle of $18 ^ { \circ }$ each second. If the pendulum is $20 \mathrm {~cm}$ in length and the complete swing from right to left lasts 2 seconds, what area is covered by each complete swing? Round to the nearest hundredth.

Find the exact circular function value. - $\csc \frac { - 2 \pi } { 3 }$

Find the exact value without using a calculator. - $\sec \frac { 3 \pi } { 4 }$

Find the exact values of s in the given interval that satisfy the given condition. - $[ 0,2 \pi ) ; \sin s = \frac { \sqrt { 3 } } { 2 }$

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - $- 13 \pi$

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - $- \frac { \pi } { 4 }$