4.1 Radian and Degree Measure

I. Angles (2 rays: an Initial side & a Terminal side).

A) Initial side = the starting ray of the angle.

1) It is on the + x-axis (from the origin).

B) Terminal side = the ending ray of the angle.

1) + angles go counter-clockwise.

2) – angles go clockwise.

C) This is known as the angle in standard position

(initial side starts at the x-axis).

4.1 Radian and Degree Measure

II. Radians and Radian Measure.

A) Radian: a way of measuring angles ( symbol θ ).

1) a radian is the ratio of the arc length (s) to

the radius (r) of the angle.

a) θ = s/r b) it is measured in terms of π.

B) One revolution = 360° = 2π radians.

C) Finding co-terminal angles (2 angles that end in

the same place).

1) Add or subtract 2π from the given angle.

D) Complimentary & Supplementary angles: 2 <‘s that add to

1) 90° or π/2 = comp. 2) 180° or π = supple.

4.1 Radian and Degree MeasureIII. Special Radian / Degree Angle Measurements.

30° 60° 90° 120° 150° 180° 210° 240° 270° 300° 330° 360°

6

6

26

36

46

56

66

76

86

96

106

116

12

3

2

3

2 3

42

33

5 2

45° 90° 135° 180° 225° 270° 315° 360°

4

4

24

34

44

54

64

74

8

22

2

3

4.1 Radian and Degree Measure

IV. Converting Degrees to Radians.

A) Since 360° = 2π radians, then 180° = π radians.

B) Convert using proportions.

1) Degrees to Radians 2) Radians to Degrees

x = (degree) x = (radians)

HW: page 290 # 2 – 52 even

x π

degree 180°

radians π

x 180°

180

180