1. Aim: How do we define radians and develop the formula
Do Now: 1. The radius of a circle is 1. Find, in terms of
the circumference.
2. What units do we use for measuring a) length
b) weight c) angle?
HW: p.405 # 28,30,32,34,36,38,39,40,42,43

2. Another unit to measure angle is the radian
Radian is the central angle that intercepts an arc whose length is the same as the radius.

3. If we choose a circle with a radius of 1, the circle is referred to as a unit circle.
If the central angle of the unit circle intercepts an arc with length 1 then the measure of the central angle is 1 radian.

4. O 
r = 1
1 radian
Arc length = 1
The circle has radius equals 1. The central of the circle that intercepts the arc with length 1 is equal to 1 radian
Use the same reason, if the radius is 2 units then the central angle equals 1 radian when the intercepted arc is also 2 units

5. One circle = 360° (degrees)
One circle = 2π radians
1π radians = 180°
90  /2 radians
270  3/2 radians

6. The length of an arc can be found by using the formula, s=rθ, where:
Arc Length
The length of an arc can be found by using the formula, s=rθ, where:
‘s’ is the length of the arc.
‘ r ‘ is the radius of the circle.
‘θ ‘ is the radian measure of the central angle.

7. Examples:
a) Find the length of an arc that subtends a central angle of 5π/6 in a circle with radius of 12 cm.
s = rθ =12⋅5π/6 = 10π ≈ cm
b) Find the radius of a circle, if the arc length is 10 and the central angle equals 2 radians.
10 / 2 = 5
c) If the radius of a circle is 15, find the central angle when the arc length equals 45.
45/15 = 3 radians