Objectives - ehsprecalc.files.wordpress.com · 05.04.2014 · April 03, 2014 Mar 27-5:13 AM...

5.1 Arc length, area sector, vocab, coterminal, reference angles_JB-A Block.notebook

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April 03, 2014

Apr 4-10:35 AM

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


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April 03, 2014

Mar 24-9:08 PM

Convert 2 radians to degrees.

Convert 35 degrees to radians

Convert -117o 30ʹ 12ʺ to degrees-decimal

Convert 315.2458 to degrees, minutes, seconds


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April 03, 2014

Mar 24-9:56 PM

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 = 2πrA = πr2


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April 03, 2014

Mar 24-10:01 PM

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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April 03, 2014

Mar 24-10:08 PM

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


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April 03, 2014

Mar 24-10:11 PM

Formulas:


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April 03, 2014

Mar 24-10:11 PM

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 diagramsSome you need to add diagramsFill in the formulas for arc length & area of a sectorCut-out or match for notes pages.


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April 03, 2014

Mar 24-10:16 PM

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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Mar 24-11:11 PM


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Mar 27-7:16 AM


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Mar 27-7:18 AM


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April 03, 2014

Mar 27-7:18 AM


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April 03, 2014

Mar 27-7:19 AM


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April 03, 2014

Mar 27-7:40 AM


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April 03, 2014

Mar 24-10:23 PM

in a circle of radius 2


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April 03, 2014

Mar 24-10:24 PM

π in a circle of diameter 20 cm.


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April 03, 2014

Mar 24-10:25 PM

degree


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April 03, 2014

Mar 24-10:25 PM

its central angle,


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April 03, 2014

Mar 24-9:10 PM

Example: A central angle, θ (theta), is subtended by an arc 10 cm long on a circle with radius 4 cm.

Find the measure of θ in degrees.Find the area of the sector formed by theta.


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April 03, 2014

Mar 24-9:10 PM

Example: A sector of a circle has arc length 6 cm and area 75 cm2.

Find the radiusFind the measure of the central angle


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April 03, 2014

Mar 24-9:54 PM

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.


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April 03, 2014

Mar 24-9:55 PM

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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April 03, 2014

Mar 24-10:21 PM

in closing...what did you find interesting?what do you need more help with?what are you confident about?


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April 03, 2014

Apr 1-7:21 AM


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April 03, 2014

Mar 27-4:49 AM

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

OBJECTIVES:


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April 03, 2014

Mar 27-4:56 AM

What is coterminal?

How would you determine a coterminal angle?


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April 03, 2014

Mar 27-4:56 AM

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.


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April 03, 2014

Mar 27-4:59 AM

Find a negative angle coterminal with

whose absolute value is larger than 5 revolutions.


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April 03, 2014

Mar 27-5:00 AM

Convert 15o30'45" to radians.


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April 03, 2014

Mar 27-5:02 AM

Are 90o and 89o 59' 60" equivalent?

- how do you know?

Find an angle complementary to 17o4'12"


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April 03, 2014

Mar 27-5:04 AM

Where does the terminal side lie for


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April 03, 2014

Mar 27-5:06 AM

Draw = -1.8 in standard position


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April 03, 2014

Mar 27-5:11 AM

Draw = 5 in standard position


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Apr 2-7:21 AM


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Apr 2-7:24 AM


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Apr 2-7:29 AM


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April 03, 2014

Mar 27-5:13 AM

Determine the reference angle for:


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April 03, 2014

Mar 27-5:16 AM

Progress Check

1. Determine the quadrant in which the terminal side lies.o /5

b. -213o 52'10"

4. Change -14

a. -163o /3

/5


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April 03, 2014

Mar 27-5:18 AM

Example: If each angle has the given measure and is in standard position, determine the quadrant in which its terminal side lies.

a. π b. 2π 6 3

c. 15π d. -4π 4 3


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April 03, 2014

Mar 27-5:18 AM

Example 7: State whether each pair of angles is coterminal. Write yes or no.

a. b.


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April 03, 2014

Mar 27-5:19 AM

Find the measure of the reference angle for each angle.

a. b.

c. d.


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Mar 31-7:27 AM


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Feb 20-3:17 PM


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Mar 27-5:19 AM

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Objectives - ehsprecalc.files.wordpress.com · 05.04.2014 · April 03, 2014 Mar 27-5:13 AM...

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