Radian Measure


Radian Measure divides a circle in 2π

*Remember:

π: ratio between circumference of a circle to its diameter

unit_circle_arc_length.jpg

in a unit circle (where r=1):
angle = arc length

in a non-unit circle:
arc length = radius x angle in radians
a = rƟ

Converting angles:

2π = 360°
π = 180°

Radians --> degrees
Ex. 1
Ɵ = 5π/4

Ɵ = 5π/4 x 180°/π

Ɵ = 225°


Ex. 2
Ɵ = 11π/6
Ɵ = 11π/6 x 180°/π
Ɵ = 330°

Degrees --> Radians
Ex. 1
135° x π/180°
(reduce)
= 3π/4

Ex. 2
200° x π/180°
(reduce)
= 10π/9

Practise: Find the following

1) sin 2π/7
2) cos π/3

Answers:
1) 0.78 2) 0.5

HOMEWORK: pg. 321 #5-8