5.1 arc length, area sector, vocab, coterminal, … · 5.1 arc length, area sector, vocab,...

5.1Arclength,areasector,vocab,coterminal,referenceangles_JBABlock.notebook

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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


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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


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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:


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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.


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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.


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Mar277:18AM


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Mar277:40AM


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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.


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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.


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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:


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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?


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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


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Mar274:49AM

Calculate angle values - coterminal, reference, complementary, & supplementary angles.

OBJECTIVES:

Mar274:56AM

What is coterminal?

How would you determine a coterminal angle?


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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.


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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"


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Mar275:04AM

Where does the terminal side lie for

Mar275:06AM

Draw = -1.8 in standard position


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Draw = 5 in standard position

Apr27:21AM


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Apr27:29AM


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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


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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


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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.


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Mar317:59AM


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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

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5.1 arc length, area sector, vocab, coterminal, … · 5.1 arc length, area sector, vocab,...

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