4 1 Radians Degrees 02

8/2/2019 4 1 Radians Degrees 02

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Sketch each of the following angle measurements. To

do so, start by drawing a circle with the x- and y-axes,

and then put your angle into standard position. Doboth on the same circle.

1. 210 2. 150


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Weve already figuredout that we canhave angles withmeasures greaterthan 180. But wecan just as easily

have angles withmeasures greaterthan 360, just askShaun White.

We can totally

have angles

greater than

360.
http://www.youtube.com/watch?v=6Uxoeh-Blqs


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What does a 390 angle look like?

It looks just like a 30 angle, except it has made a full

revolution.


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Objectives:

1. To find coterminal,

complementary, andsupplementaryangles

2. To convert between

degrees and radians3. To find arc length,

angular speed, andarea of a sector

Assignment:

P. 290: 17-20 S

P. 291: 21-24 S

P. 291: 39-42 S

P. 291: 47-50 S

P. 291: 51-54 S

P. 291: 55-70 S

P. 292: 79-94 S

P. 292-3: 101, 103, 106


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Both 30 and 390 have

terminal rays in the

same position, assuch they are called

coterminal angles.

From Exercise 1, 210and 150 were also

coterminal angles.


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Angles that have the same

initial and terminal sides are

called coterminal angles. Coterminal angles can be

found by adding or

subtracting a multiple of 360

Any angle has infinitely many

coterminal angles


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Draw each of the following angles. Give both a

positive and a negative coterminal angle for

each.1. 135 2. 50


8/43

Angles that have the same

initial and terminal sides are

called coterminal angles. Coterminal angles can be

found by adding or

subtracting a multiple of 2

Any angle has infinitely many

coterminal angles


9/43

Draw each of the following angles. Give both a

positive and a negative coterminal angle for

each.1. 5/3 2. 11/4


10/43

In trigonometry, theres acircle with radius oneunit that isuncommonly useful.Weve already laid thefoundation for this unit

circle. Lets nowtransfer all of thathard-won knowledgeto a nifty worksheet.


11/43

Convert the following radian measures to

degree measures.

1. 180

2. 603. 150

4. 210

5. 225

6. 3307. 360

8. 361


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degree measures.

1.

2. /33. /6

4. 4/3

5. 7/4

6. 11/67. 2

8. 1


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When the angle measure we are converting lies

on our unit circle, its elementary to change

units. Sometimes, however, it would be moreconvenient to use the conversion factor

below:

radians = 180Now you could set up a proportion or do

something with train tracks.


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Convert the following degree measures to

radian measures.

1. 120

2. 300

3. 80

4. 361


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degree measures.

1. 3/4

2. 3/5

3. 3

4. 1


16/43

9043

9021

mm

mm

18087

18065

mm

mm


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2/43

2/21

mm

mm

87

65

mm

mm


18/43

If possible, find the complement and the

supplement of each angle.

1. /6

2. 5/6


19/43

Find the missing angle measure in radians.

1. 2.


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The measure of an arc

is the measure of the

central angle itintercepts. It is

measured in degrees.


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An arc length is a

portion of the

circumference of acircle. It is measured

in linear units and

can be found usingthe measure of the

arc.


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Arc measure = mC

Amount of rotation

Arc length:

Actual length

2360

m Cs r


23/43

Find the measure and the length of arc AB.


24/43

The formula for arc length as learned in

geometry (and 2 slides ago) assumed the

central angle was in degrees. Convert thisformula to radians.


25/43

When the central angle

of a circle is

measured in radians,then the length s of

the arc that

intercepts

iss r


26/43

Find the measure and the length of arc AB.


27/43

Find the measure of.


28/43

For this activity

everyone needs to

stand up and holdyour arms out

perpendicular to your

body. Now rotatearound 360 at a rate

of 45 every second.

Censored


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Now that you are goodand dizzy, answer this

question: As youwere spinningaround, what had agreater speed, your

elbows or yourfingertips? Or werethey traveling at thesame speed?

Censored


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Since your fingertips andyour elbows arrived atthe same location atthe same time, andsince your fingertipshad further to travel, itmakes sense that theytraveled faster thanyour elbows. This islinear speed.

Censored


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On the other hand, therate at which you wererotating, /4 radiansper second, is angularspeed.

Linear speed is how fast

your fingertips move.Angular speed is how fast

the angle swept byyour arm changes.

Censored


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The linear speed v of a particle traveling at a

constant rate along a circular arc of radius r

and length s is:arc length

time

sv

t


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Find the linear speed of

the tip of each hand

of the clock. (In caseyou were wondering,

the time is 3:10:50,

and schools nearlyout.)


34/43

The angular speed (omega) of a particle

traveling at a constant rate along a circular arc

of measure (in radians) iscentral angle

time t


35/43

Find the angular speed

of the tip of each

hand of the clock. (Incase you were

wondering, the time

is still 3:10:50.)


36/43

Try not to vomit: A Ferris wheel with a 50-foot

radius makes 1.5 revolutions per minute. Find

the angular speed of the Ferris wheel inrad/min and the linear speed in ft/min.


37/43

Whereas an arc was a

fraction of a circles

circumference, asector is a fraction of

a circles area.

A sectors is like a pieceof pizza, while an arc

is just the crust.


38/43

When your central

angle is in degrees,

the area A of a sectoris

2

360

m CA r


39/43

Find the area of the sector swept out a minute

hand of a clock with a radius of 9 inches over

the course of 12 minutes.


40/43

The formula for the area of a sector as learned

in geometry (and 2 slides ago) assumed the

central angle was in degrees. Convert thisformula to radians.


41/43

When the central

angle of a circle of

radius r is measuredin radians, then the

area A of the sector

is

21

2A r


42/43

A large pizza from Papa

Johns has a diameter

of 14 inches. Whatsthe area of the sector

formed by 3 pieces of

pizza if their tips trace

out an angle

measuring 2/3

radians?


43/43

Objectives:

1. To find coterminal,complementary, andsupplementaryangles

2. To convert betweendegrees and radians

3. To find arc length,angular speed, andarea of a sector

Assignment:

P. 290: 17-20 S

P. 291: 21-24 S

P. 291: 39-42 S

P. 291: 47-50 S

P. 291: 51-54 S

P. 291: 55-70 S P. 292: 79-94 S

P. 292-3: 101, 103, 106

Homework Supplement

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4 1 Radians Degrees 02