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Warm-Up 8/19. Convert Angle to the other measurement 1. – 150 2. = 45. Q&A on assignment. Rigor: You will learn how to find Arc Length, Linear and Angular Speed plus the Area of a Sector . Relevance: You will be able to use angle measure to solve application problem. - PowerPoint PPT Presentation
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Warm-Up 8/19
Q&A on assignment.
Convert Angle to the other measurement
1. – 150
2. 𝜋4 = 45
¿− 5𝜋6( 𝜋 radians180 ° )( 180 °𝜋 radians )
Rigor:You will learn how to find Arc Length, Linear and Angular Speed plus the
Area of a Sector .
Relevance:You will be able to use angle measure
to solve application problem.
4-2b Degrees and Radians
Example 4: Find the length of the intercepted arc given central angle and radius. Round to the nearest tenth.
a. , r = 4 in.
b. 125, r = 7cm
𝑠=𝑟 𝜃𝑠=(4 ) 𝜋
3𝑠=4.18879
𝜃=25𝜋36
𝑠=(7 ) 25𝜋36
𝑠=15.2716
𝑠=𝑟 𝜃
𝑠=15.3𝑐𝑚
𝑠=4.2 𝑖𝑛 .
Linear Speed applies to any object that moves.
Angular Speed applies to objects that rotate.
= 2 Revolutions
𝑣=𝑟 𝜃𝑡
Example 5: Find the rotation in revolutions per minute given the angular speed.
a.
Find the radius given the linear speed and the rate of rotation.
b.
𝜔=260𝜋 𝑟𝑎𝑑h260𝜋 2𝜋
130 𝑟𝑒𝑣h
= 2 Revolutions
∙ h60𝑚𝑖𝑛
≈2.17 𝑟𝑒𝑣𝑚𝑖𝑛
𝑣=14137 𝑖𝑛𝑚𝑖𝑛 ,2.5 𝑟𝑒𝑣𝑠
𝑣=𝑠𝑡=
𝑟 𝜃𝑡
𝜔=𝜃𝑡
14137 𝑖𝑛𝑚𝑖𝑛 ∙𝑚𝑖𝑛
60 𝑠
2 π ∙2.5 𝑟𝑒𝑣𝑠 =5𝜋 𝑟𝑎𝑑𝑠
¿235.617 𝑖𝑛
𝑠
235.617 𝑖𝑛𝑠 =
𝑟 5𝜋𝑠
𝑠5𝜋 ∙ ∙ 𝑠5𝜋
14.9998≈𝑟
Area of a SectorThe area A of a sector of a circle with radius r and central angle is
where is measures in radians.
Example 6: Find Area of Sector.𝐴=
12 𝑟
2𝜃
𝜃=60 ° 𝜋180 ° ¿
𝜋3
𝑟=8 𝑓𝑡
𝐴=12 8
2 𝜋3
𝐴=32𝜋3 ≈33.5 𝑓𝑡 2
√−1math!
4-2a Assignment: TX p238, 27-39 odd + 43-47 odd
Unit 1 TestThursday 8/22