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