-
5.1Arclength,areasector,vocab,coterminal,referenceangles_JBABlock.notebook
1
May14,2014
Apr410:35AM
5.1 & 5.4
Objectives: Generate vocabulary flashcards for new terms. Derive
formulas for arc length and area of a circular
sector. Solve application problems using the arc length and area
of
circular sector formulas.
Know, Do List
Mar249:08PM
Convert2radianstodegrees.
Warmup:
Convert35degreestoradians
Convert117o3012todegreesdecimal
Convert315.2458todegrees,minutes,seconds
-
5.1Arclength,areasector,vocab,coterminal,referenceangles_JBABlock.notebook
2
May14,2014
Mar249:56PM
Example:A pizza vendor sells a small slice for $2 and a large
slice for $3. The small slice is 1/6 of pizza with diameter of 18"
and the large slice is 1/8 of a pizza with diameter of 26".
Which slice is the better buy?
How many inches of crust (crust length) would you eat if you ate
a slice from the pizza with an 18"diameter?
hint: C = 2rA = r2
Mar2410:01PM
Arc length is the measure of an arc of a circle.
The crust from the previous example represents an arc
length.
Generate a formula that you could use when you wanted to
determine arc length.
Let s = arc length
-
5.1Arclength,areasector,vocab,coterminal,referenceangles_JBABlock.notebook
3
May14,2014
Mar2410:08PM
Area of a circular sector is the area of a portion of a
circle.
The area of a slice of pizza from the previous example
represents area of a sector.
Generate a formula that you could use when you wanted to
determine area of a sector.
Let A = area of the sector
Mar2410:11PM
Formulas:
-
5.1Arclength,areasector,vocab,coterminal,referenceangles_JBABlock.notebook
4
May14,2014
Mar2410:11PM
Before completing more examples let's get to know the
terminology.... In small groups you will use the
flashcards, wordbank, your book, and/or devices to match
definitions with terms.
Some terms have diagrams Some you need to add diagrams Fill in
the formulas for arc length & area
of a sector Cut-out or match for notes pages.
Mar2410:16PM
We will review some terms as a group before practice
problems.
When finished you may verify yours with my answer key.
After finalizing your flashcards, fill in the unit circle with
radian measures.
On an index card answer one of the following questions.
-
5.1Arclength,areasector,vocab,coterminal,referenceangles_JBABlock.notebook
5
May14,2014
Mar2411:11PM
1. Howwouldyouexplainyoursolutiontosomeoneelse?2.
Howdoesthisproblemconnecttootherproblems?3.
Whatwouldasimilarproblemlooklike?4.
Howdidyoudeterminewhattodiagram?5. Howdidyoudecidewhattodraw?6.
Whatinformationdidyouusetostartthisproblem?7.
Whatinformationhelpedyousolvethisproblem?8.
Whatisinterestingaboutthisproblem?9.
Couldyouhavesolvedthisinasimplerway?10.
Howelsecouldyouhavesolvedthis?11.
Whywereyouaskedtosolvethisproblem?12.
Whatwouldasimilarproblemask?13. Howwouldyourestatethisproblem?14.
Howwouldyousummarizeyourapproachtothisproblem?
Mar277:16AM
Objectives:
finalizevocabularyapplynewterms.
-
5.1Arclength,areasector,vocab,coterminal,referenceangles_JBABlock.notebook
6
May14,2014
Mar277:18AM
Mar277:18AM
-
5.1Arclength,areasector,vocab,coterminal,referenceangles_JBABlock.notebook
7
May14,2014
Mar277:19AM
Mar277:40AM
-
5.1Arclength,areasector,vocab,coterminal,referenceangles_JBABlock.notebook
8
May14,2014
Mar2410:23PM
Example: Given is the measure of a central angle, find the
measure of its intercepted arc in terms of in a circle of radius 20
cm.
Mar2410:24PM
Example: a. Find the length of an arc that subtends a central
angleof 99o in a circle of radius 10 cm.
b. Given the measurement of the central angle is 135o , find the
measure of its intercepted arc in terms of in a circle of diameter
20 cm.
-
5.1Arclength,areasector,vocab,coterminal,referenceangles_JBABlock.notebook
9
May14,2014
Mar2410:25PM
Example: Given the measure of an arc is 5 units, find the degree
measure to the nearest second of the central angle it subtends in a
circle of radius 8 cm.
Mar2410:25PM
Example: Find the area of the sector to the nearest tenth, given
its central angle, , and the radius of the circle.
= 5 r = 10 ft 12
Example: A sector has arc length 16 cm and a central angle
measuring 0.95 radians. Find the radius of the circle and the area
of the sector.
-
5.1Arclength,areasector,vocab,coterminal,referenceangles_JBABlock.notebook
10
May14,2014
Mar249:10PM
Example: A central angle, (theta), is subtended by an arc 10 cm
long on a circle with radius 4 cm.
Find the measure of in degrees. Find the area of the sector
formed by theta.
Mar249:10PM
Example: A sector of a circle has arc length 6 cm and area 75
cm2.
Find the radius Find the measure of the central angle
homeworkworksheet:
-
5.1Arclength,areasector,vocab,coterminal,referenceangles_JBABlock.notebook
11
May14,2014
Mar249:54PM
ex: Suppose a wheel with diameter of 24 inches is rotating at
800 rpm.
Find the angular speed of the wheel in degrees and radians.
Calculate the speed of the vehicle that the wheel is attached
to.
Mar249:55PM
ex: The geographic and magnetic north poles have different
locations. Currently the magnetic north pole is drifting westward
through 0.0017 radian per year, where the vertex of the drift angle
is at the center of the earth. If this movement continues, how long
will it take for the magnetic north pole to drift a total of
5o?
-
5.1Arclength,areasector,vocab,coterminal,referenceangles_JBABlock.notebook
12
May14,2014
Mar2410:21PM
HomeworkPg369#9,11,16,31,33,35,41,48
in closing...what did you find interesting?what do you need more
help with?what are you confident about?
Apr17:21AM
-
5.1Arclength,areasector,vocab,coterminal,referenceangles_JBABlock.notebook
13
May14,2014
Mar274:49AM
Calculate angle values - coterminal, reference, complementary,
& supplementary angles.
OBJECTIVES:
Mar274:56AM
What is coterminal?
How would you determine a coterminal angle?
-
5.1Arclength,areasector,vocab,coterminal,referenceangles_JBABlock.notebook
14
May14,2014
Mar274:56AM
Find a negative angle that is coterminal with 100o.
Find a positive angle that is coterminal with 100o but that is
also larger than 3 revolutions.
Mar274:59AM
Find a negative angle coterminal with
whose absolute value is larger than 5 revolutions.
-
5.1Arclength,areasector,vocab,coterminal,referenceangles_JBABlock.notebook
15
May14,2014
Mar275:00AM
Convert 15o30'45" to radians.
Mar275:02AM
Are 90o and 89o 59' 60" equivalent?
- how do you know?
Find an angle complementary to 17o4'12"
-
5.1Arclength,areasector,vocab,coterminal,referenceangles_JBABlock.notebook
16
May14,2014
Mar275:04AM
Where does the terminal side lie for
Mar275:06AM
Draw = -1.8 in standard position
-
5.1Arclength,areasector,vocab,coterminal,referenceangles_JBABlock.notebook
17
May14,2014
Mar275:11AM
Draw = 5 in standard position
Apr27:21AM
-
5.1Arclength,areasector,vocab,coterminal,referenceangles_JBABlock.notebook
18
May14,2014
Apr27:24AM
Apr27:29AM
-
5.1Arclength,areasector,vocab,coterminal,referenceangles_JBABlock.notebook
19
May14,2014
Mar275:13AM
Determine the reference angle for:
Mar275:16AM
Progress Check
1. Determine the quadrant in which the terminal side lies.a.
205o b. 2/5
2. Change to a decimal number of degrees to the nearest
thousandth.a. 15o 22'35" b. -213o 52'10"
3. Change 175o to radian measure in terms of .
4. Change -14/5 to degree measure rounded to the nearest
minute.
5. Find one positive angle and one negative angle that are
coterminal with each angle.
a. -163o b. 2/3
6. Find the reference angle for each angle with the given
measure.a. 400o b. 24/5
-
5.1Arclength,areasector,vocab,coterminal,referenceangles_JBABlock.notebook
20
May14,2014
Mar275:16AM
Progress Check
1. Determine the quadrant in which the terminal side lies.a.
205o b. 2/5
2. Change to a decimal number of degrees to the nearest
thousandth.a. 15o 22'35" b. -213o 52'10"
3. Change 175o to radian measure in terms of .
4. Change -14/5 to degree measure rounded to the nearest
minute.
5. Find one positive angle and one negative angle that are
coterminal with each angle.
a. -163o b. 2/3
6. Find the reference angle for each angle with the given
measure.a. 400o b. 24/5
Mar275:18AM
Example: If each angle has the given measure and is in standard
position, determine the quadrant in which its terminal side
lies.
a. b. 2 6 3
c. 15 d. -4 4 3
-
5.1Arclength,areasector,vocab,coterminal,referenceangles_JBABlock.notebook
21
May14,2014
Mar275:18AM
Example 7: State whether each pair of angles is coterminal.
Write yes or no.
a. b.
Mar275:19AM
Find the measure of the reference angle for each angle.
a. b.
c. d.
-
5.1Arclength,areasector,vocab,coterminal,referenceangles_JBABlock.notebook
22
May14,2014
Feb203:17PM
Mar317:59AM
-
5.1Arclength,areasector,vocab,coterminal,referenceangles_JBABlock.notebook
23
May14,2014
Mar318:05AM
Mar317:27AM
-
5.1Arclength,areasector,vocab,coterminal,referenceangles_JBABlock.notebook
24
May14,2014
Feb203:17PM
Feb203:17PM
-
5.1Arclength,areasector,vocab,coterminal,referenceangles_JBABlock.notebook
25
May14,2014
Mar275:19AM
-
Attachments
5.1BKnowDo.docx
L1 Pre-Calculus
Section 5.1B Sectors of Circles
By the end of this section you should know:
the definition of and parts of a sector of a circle
formulas for arc length of a sector
formulas for area of a sector
By the end of this section you should be able to:
find central angle of a sector given a variety of
information
find arc length of a sector given a variety of information
find area of a sector given a variety of information
solve applied problems
SMART Notebook
Page 1Page 2Page 3Page 4Page 5Page 6Page 7Page 8Page 9Page
10Page 11Page 12Page 13Page 14Page 15Page 16Page 17Page 18Page
19Page 20Page 21Page 22Page 23Page 24Page 25Attachments Page 1