5.1 Arc length, area sector, vocab, coterminal, reference angles_jb A Block.notebook May 14, 2014

Transcription

1 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 5.1 & 5.4 Apr 4 10:35 AM Warm up: Convert to degrees, minutes, seconds Convert 117 o 30ʹ 12ʺ to degrees decimal Convert 35 degrees to radians Convert 2 radians to degrees. Mar 24 9:08 PM 1

2 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 = 2πr A = πr 2 Mar 24 9:56 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 Mar 24 10:01 PM 2

3 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 Mar 24 10:08 PM Formulas: Mar 24 10:11 PM 3

4 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. Mar 24 10:11 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. Mar 24 10:16 PM 4

5 1. How would you explain your solution to someone else? 2. How does this problem connect to other problems? 3. What would a similar problem look like? 4. How did you determine what to diagram? 5. How did you decide what to draw? 6. What information did you use to start this problem? 7. What information helped you solve this problem? 8. What is interesting about this problem? 9. Could you have solved this in a simpler way? 10. How else could you have solved this? 11. Why were you asked to solve this problem? 12. What would a similar problem ask? 13. How would you restate this problem? 14. How would you summarize your approach to this problem? Mar 24 11:11 PM Objectives: finalize vocabulary apply new terms. Mar 27 7:16 AM 5

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7 Mar 27 7:19 AM Mar 27 7:40 AM 7

8 Example: Given is the measure of a central angle, find the measure of its intercepted arc in terms of π in a circle of radius 20 cm. Mar 24 10:23 PM Example: a. Find the length of an arc that subtends a central angle of 99 o in a circle of radius 10 cm. b. Given the measurement of the central angle is 135 o, find the measure of its intercepted arc in terms of π in a circle of diameter 20 cm. Mar 24 10:24 PM 8

9 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. Mar 24 10:25 PM Example: Find the area of the sector to the nearest tenth, given its central angle, θ, and the radius of the circle. θ = 5π 12 r = 10 ft 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. Mar 24 10:25 PM 9

10 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. Mar 24 9:10 PM Example: A sector of a circle has arc length 6 cm and area 75 cm 2. Find the radius Find the measure of the central angle homework worksheet: Mar 24 9:10 PM 10

11 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. Mar 24 9:54 PM ex: The geographic and magnetic north poles have different locations. Currently the magnetic north pole is drifting westward through 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 5 o? Mar 24 9:55 PM 11

12 Homework Pg 369 #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? Mar 24 10:21 PM Apr 1 7:21 AM 12

13 OBJECTIVES: Calculate angle values - coterminal, reference, complementary, & supplementary angles. Mar 27 4:49 AM What is coterminal? How would you determine a coterminal angle? Mar 27 4:56 AM 13

14 Find a negative angle that is coterminal with 100 o. Find a positive angle that is coterminal with 100 o but that is also larger than 3 revolutions. Mar 27 4:56 AM Find a negative angle coterminal with whose absolute value is larger than 5 revolutions. Mar 27 4:59 AM 14

15 Convert 15 o 30'45" to radians. Mar 27 5:00 AM Are 90 o and 89 o 59' 60" equivalent? - how do you know? Find an angle complementary to 17 o 4'12" Mar 27 5:02 AM 15

16 Where does the terminal side lie for Mar 27 5:04 AM Draw = -1.8 in standard position Mar 27 5:06 AM 16

17 Draw = 5 in standard position Mar 27 5:11 AM Apr 2 7:21 AM 17

18 Apr 2 7:24 AM Apr 2 7:29 AM 18

19 Determine the reference angle for: Mar 27 5:13 AM Progress Check 1. Determine the quadrant in which the terminal side lies. a. 205 o b. 2π/5 2. Change to a decimal number of degrees to the nearest thousandth. a. 15 o 22'35" b o 52'10" 3. Change 175 o to radian measure in terms of π. 4. Change -14π/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 o b. 2π/3 6. Find the reference angle for each angle with the given measure. a. 400 o b. 24π/5 Mar 27 5:16 AM 19

20 Progress Check 1. Determine the quadrant in which the terminal side lies. a. 205 o b. 2π/5 2. Change to a decimal number of degrees to the nearest thousandth. a. 15 o 22'35" b o 52'10" 3. Change 175 o to radian measure in terms of π. 4. Change -14π/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 o b. 2π/3 6. Find the reference angle for each angle with the given measure. a. 400 o b. 24π/5 Mar 27 5:16 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 Mar 27 5:18 AM 20

21 Example 7: State whether each pair of angles is coterminal. Write yes or no. a. b. Mar 27 5:18 AM Find the measure of the reference angle for each angle. a. b. c. d. Mar 27 5:19 AM 21

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26 Attachments 5.1B Know Do.docx