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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
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
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
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!!!
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
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!!!