1. Chapter 4-2: Lengths of Arcs and Areas of Sectors

2. Review Let’s remember what an Arc is… So…. Geometrically, what is an Arc? A B AB This is a central angle: An angle whose vertex is in the center of the circle.

3. Question: Find an arc length with the central angle of 90˚ and the radius = 4? How about 60˚? How about 50˚?

4. Arc Length Arc Length: Portion of the Circumference Let s = Arc Length Let θ = Angle Measure Then: Arc Length or s = r θ s = WARNING: θ has to be in radians θ is in degrees

5. Example: Find the length of an arc of a 105° central angle in a circle of radius 3 ft. s = You try: Find the length of an arc with a central angle of 5π/4 whose radius is 2 inches.

6. Review Let’s remember what a Sector is… So…. Geometrically, what is an Sector? A B AB This is a sector:

7. Question: Find the area of the sector with the central angle of 90˚ and the radius = 4? How about 60˚? How about 50˚?

8. Area of Sectors Sector: Portion of the Area Let A = Area of Sector Then: Area of Sector or A = A = WARNING : θ is in radians θ is in degrees

9. Example: Find the area of a sector of a circle of radius 4 cm if the central angle is 4π/3. A = You try: Find the area of a sector of a circle with a central angle of 36° whose radius is 9 mm.

10. Application… A water irrigation arm 300 ft. long rotates once each day. How much irrigation area is covered in 1/3 of the day? Q: First ask is it length or area? Q: Next ask the unit of measure you are in? So.. Pick one, and use the right formula!