1. Warm Up
Write an equation for a cosine function with the following characteristics. Amplitude: 4 Period:  Phase shift: left 3 Vertical shift: down 4

2. Answer
Write an equation for a cosine function with the following characteristics. Amplitude: 4 Period:  y = 4 cos (2x + 3) - 4 Phase shift: left 3 Vertical shift: down 4

3. Arc length
and
Sector area

4. Arc Length
An arc is a portion of a circle’s circumference. θ

5. Θ must always be in radians!
Arc Length
s = arc length r = radius θ = central angle
s = rθ
Θ must always be in radians!

6. Example 1: Arc Length
Find the length of the arc of a circle of radius 4 meters subtended by a central angle of 0.5 radian.

7. Sector Area
A sector is a portion of the circle’s area. θ

8. Θ must always be in radians!
Sector Area
A = sector area
r = radius
θ = central angle
A = ½r2θ
Θ must always be in radians!

9. Example 2: Area of a Sector
Find the area of the sector of a circle of radius 5 feet subtended by an angle of 60°. Round the answer to two decimal places.

10. Put it all together! Arc Length s = rθ Length of crust
Sector Area A = ½r2θ Area of slice