Chapter 13 Section 3

Radian Measure

Central Angle

• Central Angle = Intercepted Arc

1 unit

(1,0)

1 Radian

• Central Angle when the Radius = Arc Length

(1,0)1 radian

To convert Degrees to Radiansor Radians to Degrees

rd o

180

To convert 1200 to Radiansor Radians to Degrees

ro

180

120

r180120

r

120 r3

2

To convert 1200 to Radiansor Radians to Degrees

ro

180

120

r180120

r

120 r3

2

Unit CircleFor angles in standard position we use the variable

to show we are talking about an angle

1 unit

(1,0)

(

For any point on the unit circle, we can find the coordinates by using the angle in standard position and the rule

(cos() , sin())

1 unit

(1,0)

(cos() , sin())

Cosine and Sine of 30-60-90 triangles

1

2

3

Sin (30)

Cos (30)

Cosine and Sine of 30-60-90 triangles

1

2

3

Sin (60)

Cos (60)

300

Cosine and Sine of 45-45-90 triangles

1

1

2

Sin (45)

Cos (45)

450

For angles with a terminal side not in the 1st quadrant

1 unit

(1,0)

(- , )

Make a 30-60-90 triangle and look at the coordinates

For angles with a terminal side not in the 1st quadrant use the rule QI (+,+) QII (-,+) QIII (-,-) QIV(+,-)

1 unit

(1,0)

(- ,- )

Make a 30-60-90 triangle and look at the coordinates

For angles with a terminal side not in the 1st quadrant use the rule QI (+,+) QII (-,+) QIII (-,-) QIV(+,-)

1 unit

(1,0)

( ,- )

U Try

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