2.1 Continued! Warm-up Learning Objective: To understand what a radian is and how they relate to...

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2.1 Continued! Warm-up Learning Objective: To understand what a radian is and how they relate to degrees to be able to convert radians to degrees and degrees to radians, and to learn the Area of a Sector formula and how to use it 1. Draw the angle: a. b. 2. Convert to a decimal: a. b. 3. Convert to DºM‘S“ : a. b. 4. Find the arc length of a circle with the given measures: a. b. a.9.15 b.98.38 270 99'9" 98 22'45" 225 19.99 44.01 3 ft, 1.24 radians r 1 2 m , radians 4 r a. 19 59'24" b.44 0'36" 2 a.3.72 ft 2 1 b. m 2

Transcript of 2.1 Continued! Warm-up Learning Objective: To understand what a radian is and how they relate to...

Page 1: 2.1 Continued! Warm-up Learning Objective: To understand what a radian is and how they relate to degrees to be able to convert radians to degrees and degrees.

2.1 Continued!

Warm-up

Learning Objective: To understand what a radian is and how they relate to degrees to be able to convert radians to degrees and degrees to radians, and to learn the Area of a Sector formula and how to use it

1. Draw the angle:a. b.

2. Convert to a decimal: a. b.

3. Convert to DºM‘S“ : a. b.

4. Find the arc length of a circle with the given measures: a.

b.

a. 9.15 b. 98.38

270

9 9 '9" 98 22 '45"

225

19.99 44.01

3 ft, 1.24 radiansr 1

2 m, radians4

r

a. 19 59 '24" b. 44 0 '36"

2a. 3.72 ft

21b. m

2

Page 2: 2.1 Continued! Warm-up Learning Objective: To understand what a radian is and how they relate to degrees to be able to convert radians to degrees and degrees.

Converting Degrees and Radians

1 full revolution is 360º

180º=

=

NOTES

2 radians radians

s r

Arc length of a full circle…

2c r

2 r r2

So… 1º=180 180

180

and1 radian=180

Conversion ratio!!

Ex 1 – Convert to radians

a. 60

180

3

b. 45

180

4

c. 90

180

2

d. 270

180

3

2

Page 3: 2.1 Continued! Warm-up Learning Objective: To understand what a radian is and how they relate to degrees to be able to convert radians to degrees and degrees.

Ex 2 - Convert to degrees

3a.

2

180

2707

b. 3

180

420

c. 3 radians 180

171.893If there’s no , use calc!

Area of a Sector

21

2A r MUST be in

radians!!!

Page 4: 2.1 Continued! Warm-up Learning Objective: To understand what a radian is and how they relate to degrees to be able to convert radians to degrees and degrees.

Ex 3 - Find the area of a sector within a circle with radius 2ft formed by an angle of 30º. Round to 2 decimal places.

21

2A r

A 1

2 2 2

30Have to convert to radians! 180

6

6

A 2

6

21.05 ft

Page 5: 2.1 Continued! Warm-up Learning Objective: To understand what a radian is and how they relate to degrees to be able to convert radians to degrees and degrees.

HW – p. 125 #35-40,47-52,59,60,65,66, 79-82,86-88

Out - Convert 315º to radians.

Summary - Choose one:Now I understand… or I’m not sure about…

Quiz next time!!!


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