Chapter 13 Section 2

Angles and the Unit circle

• Parts of an angle

Initial Side

Terminal Side

Vertex

Standard Position

• Vertex is at the center

• Initial side is on the + x axis

700

Standard Position

• If terminal ray is in the II quadrant

300

Standard Position

• If terminal side is in the III quadrant

200

Standard Position

• If terminal side is in the IV quadrant

400

450

110

150

Find the measure of each angle

Negative Angle

• If you measure an angle counter clockwise you call can give the angle a negative degree

-400

Co-Terminal measures

• A negative angle and + angle measure that describe the same angle are called Co- Terminal

-400 and 320o are co-terminal

Find the Co Terminal Angle

• -350

• -2000

• -3000

• -2820

• 1850

• 3300

Unit Circle

• A Circle with a radius of one unit centered on the origin

1 unit

(1,0)

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

Do Now

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