Chapter 4: Circular Functions Lesson 2: Lengths of Arcs and Areas of Sectors Mrs. Parziale.

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Presentation transcript:

Chapter 4: Circular Functions Lesson 2: Lengths of Arcs and Areas of Sectors Mrs. Parziale

Terms to know: arc length – length of a portion of a circle perimeter. (using degrees) Area of a sector – area of the portion of a circle enclosed by two radii and an arc.

Example 1: Find the length of the arc of a circle with a radius of 8 inches and a central angle of 60 °.

Using Radians Circular Arc length formula: s = arc length,  = measure of central angle (radians), r = radius. Then, Example 2: Find the length of the arc of a circle with radius 8 in. and central angle

Example 3: Find the radius of a circle if the length of an arc is and its central angle is.

Example 4: Find the area of a 45° sector of a circle with radius 11". A =

Circular Sector Area Formula Using radians: A = area of the sector,  = measure of central angle (radians), r = radius. Then,

Example 4: Now, using radians, – Find the area of a 45° sector of a circle with radius 11".

Example 6: A water irrigation arm 500 meters long rotates around pivot P once per day. How much area is irrigated every hour? Draw a diagram representing this situation.

Closure Given a circle of radius 4 meters and a central angle of 30° as shown below. Find the length of the arc. Find the area of the sector.