Sec 6.1 Angle Measure

Objectives:•To understand the difference between radian measure and degree measure.•To convert between radians and degrees.•To understand co-terminal angles and how to find them.

•To understand arc lengths and area of sectors.

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Radian Measure

If a circle of radius 1 is drawn with the vertex of an angle at its center, then the measure of this angle in radians (abbreviated rad) is the length of the arc that subtends the angle.

The circumference of the circle of radius 1 is 2π. So, a complete revolution has measure 2π rad.

Relationship between Degrees and Radians

To convert degrees to radians, multiply by .

To convert radians to degrees, multiply by .

180 radians 1801 radian

1180

radians

180

180

Ex 1. Convert the degrees to radian measure.

a) 60

b) 30

c) -54

d) -118

e) 45

Ex 2. Convert the radians to degrees.

a)

b)

c)

d)

6

2

11

18

9

Class Work

1) 30

3) 120

2)3

54)

6

180

6

180

60

180

2

3

180

150

5) 210

7) 300

46)

3

118)

6

180

7

6

180

240

180

5

3

180

330

Find the degrees or radians of each:

We define cos as the 'x' coordinate.We define sin as the 'y' coordinate.

( , )x y

Classwork: Worksheet: 5.1 Unit Circle Worksheet

Angle Measure

Angles in Standard Position

An angle is in standard position if it is drawn with its vertex at the origin and its initial side on the positive x-axis.

Coterminal Angles

• Two angles in standard position are coterminal if their sides coincide. Which angles below are coterminal?

Ex 3. Find one positive and one negative angle that is coterminal with the angle = 30° in standard position.

Ex 4. Find one positive and one negative angle that is coterminal with the angle = in standard position.

3

Class Work

Convert from degrees to radians.1. 542. -300

Convert from radians to degrees.3.

4.

11

3

13

12

Find one postive angle and one negative angle in standard position that are coterminal with the given angle.

5.135

6. 11

6

Ex 5. Find an angle with measure between 0 and 360 that is coterminal with the angle of measure 1290.

Ex 6. a) Find and angle between 0 and 2 that is coterminal with 63 .

b) Find and angle between 0 and 2 that is coterminal with .88

3

Class Work

Find an angle between 0 and 360 that is coterminal with the given angle.

7. 361

8. 1270

Find an angle between 0 and 2 that is coterminal with the given angle.

9.

10.

7

3

51

2

HW #1 p.474 (1,5,7,13,15) all, (25-45) e.o.o