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Graphical

For the following exercises, draw an angle in standard position with the given measure.

30°

300°

Graph of a circle with an angle inscribed.

−80°

135°

Graph of a circle with an angle inscribed.

−150°

2 π 3

Graph of a circle with an angle inscribed.

7 π 4

5 π 6

Graph of a circle with an angle inscribed.

π 2

π 10

Graph of a circle with an angle inscribed.

415°

−120°

240°

Graph of a circle with an angle inscribed.

−315°

22 π 3

4 π 3

Graph of a circle showing the equivalence of two angles.

π 6

4 π 3

2 π 3

Graph of a circle showing the equivalence of two angles.

For the following exercises, refer to [link] . Round to two decimal places.

Graph of a circle with radius of 3 inches and an angle of 140 degrees.

Find the arc length.

Find the area of the sector.

7 π 2 11.00  in 2

For the following exercises, refer to [link] . Round to two decimal places.

Graph of a circle with angle of 2pi/5 and a radius of 4.5 cm.

Find the arc length.

Find the area of the sector.

81 π 20 12.72  cm 2

Algebraic

For the following exercises, convert angles in radians to degrees.

3 π 4 radians

π 9 radians

20°

5 π 4 radians

π 3 radians

60°

7 π 3 radians

5 π 12 radians

−75°

11 π 6 radians

For the following exercises, convert angles in degrees to radians.

90°

π 2 radians

100°

−540°

3 π radians

−120°

180°

π radians

−315°

150°

5 π 6 radians

For the following exercises, use to given information to find the length of a circular arc. Round to two decimal places.

Find the length of the arc of a circle of radius 12 inches subtended by a central angle of π 4 radians.

Find the length of the arc of a circle of radius 5.02 miles subtended by the central angle of π 3 .

5.02 π 3 5.26 miles

Find the length of the arc of a circle of diameter 14 meters subtended by the central angle of 5 π 6 .

Find the length of the arc of a circle of radius 10 centimeters subtended by the central angle of 50°.

25 π 9 8.73 centimeters

Find the length of the arc of a circle of radius 5 inches subtended by the central angle of 220°.

Find the length of the arc of a circle of diameter 12 meters subtended by the central angle is 63°.

21 π 10 6.60 meters

For the following exercises, use the given information to find the area of the sector. Round to four decimal places.

A sector of a circle has a central angle of 45° and a radius 6 cm.

A sector of a circle has a central angle of 30° and a radius of 20 cm.

104.7198 cm 2

A sector of a circle with diameter 10 feet and an angle of π 2 radians.

A sector of a circle with radius of 0.7 inches and an angle of π radians.

0.7697 in 2

For the following exercises, find the angle between 0° and 360° that is coterminal to the given angle.

−40°

−110°

250°

700°

1400°

320°

For the following exercises, find the angle between 0 and 2 π in radians that is coterminal to the given angle.

π 9

10 π 3

4 π 3

13 π 6

44 π 9

8 π 9

Real-world applications

A truck with 32-inch diameter wheels is traveling at 60 mi/h. Find the angular speed of the wheels in rad/min. How many revolutions per minute do the wheels make?

A bicycle with 24-inch diameter wheels is traveling at 15 mi/h. Find the angular speed of the wheels in rad/min. How many revolutions per minute do the wheels make?

1320 rad 210.085 RPM

A wheel of radius 8 inches is rotating 15°/s. What is the linear speed v , the angular speed in RPM, and the angular speed in rad/s?

A wheel of radius 14 inches is rotating 0.5 rad/s. What is the linear speed v , the angular speed in RPM, and the angular speed in deg/s?

7 in./s, 4.77 RPM, 28.65 deg/s

A CD has diameter of 120 millimeters. When playing audio, the angular speed varies to keep the linear speed constant where the disc is being read. When reading along the outer edge of the disc, the angular speed is about 200 RPM (revolutions per minute). Find the linear speed.

When being burned in a writable CD-R drive, the angular speed of a CD is often much faster than when playing audio, but the angular speed still varies to keep the linear speed constant where the disc is being written. When writing along the outer edge of the disc, the angular speed of one drive is about 4800 RPM (revolutions per minute). Find the linear speed if the CD has diameter of 120 millimeters.

1 , 809 , 557.37  mm/min = 30.16  m/s

A person is standing on the equator of Earth (radius 3960 miles). What are his linear and angular speeds?

Find the distance along an arc on the surface of Earth that subtends a central angle of 5 minutes ( 1  minute = 1 60  degree ) . The radius of Earth is 3960 miles.

5.76 miles

Find the distance along an arc on the surface of Earth that subtends a central angle of 7 minutes ( 1  minute = 1 60  degree ) . The radius of Earth is 3960 miles.

Consider a clock with an hour hand and minute hand. What is the measure of the angle the minute hand traces in 20 minutes?

120 °

Extensions

Two cities have the same longitude. The latitude of city A is 9.00 degrees north and the latitude of city B is 30.00 degree north. Assume the radius of the earth is 3960 miles. Find the distance between the two cities.

A city is located at 40 degrees north latitude. Assume the radius of the earth is 3960 miles and the earth rotates once every 24 hours. Find the linear speed of a person who resides in this city.

794 miles per hour

A city is located at 75 degrees north latitude. Assume the radius of the earth is 3960 miles and the earth rotates once every 24 hours. Find the linear speed of a person who resides in this city.

Find the linear speed of the moon if the average distance between the earth and moon is 239,000 miles, assuming the orbit of the moon is circular and requires about 28 days. Express answer in miles per hour.

2,234 miles per hour

A bicycle has wheels 28 inches in diameter. A tachometer determines that the wheels are rotating at 180 RPM (revolutions per minute). Find the speed the bicycle is travelling down the road.

A car travels 3 miles. Its tires make 2640 revolutions. What is the radius of a tire in inches?

11.5 inches

A wheel on a tractor has a 24-inch diameter. How many revolutions does the wheel make if the tractor travels 4 miles?

Questions & Answers

what is photosynthesis
Victor Reply
The process plants use to convert sunlight into food (energy).
juanita
Some other organisms use
juanita
types of photosynthesis
Victor
ps1 and ps2
smritilekha
what is used to determine phylogeny?
Israel Reply
which condition is the basis for a species to be reproductively isolated from other members?
Israel Reply
Why do scientists consider vestigial structures evidence for evolution?
Israel
8.Which statement about analogies is correct?
Israel
What is true about organisms that are a part of the same clade?
Israel
Why is it so important for scientists to distinguish between homologous and analogous characteristics before building phylogenetic trees?
Israel
(CH2O)n is the stoichiometric formula of
Marcellus Reply
what are nucleotide
Anastijjaninaiya Reply
Methane,ammonia,water and sugar are dissolved to form nuceotide
Me
Introduction To Biology
Tanveer Reply
can ringworm be caused by bacterium
fred Reply
Nope
ejikeme
Branches of biology
Tanveer
no it does not occurs by bacterium
gopal
what is a brick?
Istifanus Reply
what is gene in biology?
yousaf Reply
it is a heredity unit
Me
what is DNA
yousaf Reply
carrier of genetic information
missy
deoxyribonucleic acid
gopal
it contains genetic information and brings it to one generation to other
gopal
it is of two Types circular DNA and linear DNA
gopal
plasmids are the type of small circular DNA which lies outside the genomic DNA
gopal
And what makes a virus to be difficult to destroy
Mosongo
what observation is made when dry seeds and soaked seeds are put in a vacuum flask
Robin Reply
there is respiration from the soak seeds which shows on the walls of the vacuum flask
Israel
what's mammals ?
Istifanus Reply
mammals are vertebrates ,any member group of vertebrates animals in which the young are nourished with milk from special mammary glands of the mother.
yousaf
what are actin and myosin
Praveen Reply
they are muscle filaments
Israel
they make up the microfibrils of the muscle ,relaxing and contracting to cause movement
Israel
Please did anybody know the questions that will come out in the coming practical?
Oladimeji
Why it is importantthat there are different types of protein in plasma membraine for the transport materials into and out of a cell?
Louellie Reply
the nerve cell
Mustapha Reply
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Source:  OpenStax, Essential precalculus, part 2. OpenStax CNX. Aug 20, 2015 Download for free at http://legacy.cnx.org/content/col11845/1.2
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