Trigonometry Section 7.2 Calculate arclengths and areas of a sectors Note: The arclength and the area of the sector are a fraction of the circumference.

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Presentation transcript:

Trigonometry Section 7.2 Calculate arclengths and areas of a sectors Note: The arclength and the area of the sector are a fraction of the circumference and area of the circle. A sector is “section” of a circle. Its central angle Θ can be expressed in terms of degrees or radians.

Formulas for Sectors Θ in degrees Arclength: s = Θ/360 ∙2πr Area: K = Θ/360∙πr 2 K = ½rs Θ in radians Arclength: s = rΘ Area: K = ½ r 2 Θ

Θ in degrees Θ in radians Arclength: s = Θ/360 ∙2πr Arclength: s = rΘ Area: K = Θ/360∙πr 2 Area: K = ½ r 2 Θ K = ½rs A sector of a circle has an arclength of 6 cm and an area of 75 cm 2. Find its radius and the measure of its central angle.

Θ in degrees Θ in radians Arclength: s = Θ/360 ∙2πr Arclength: s = rΘ Area: K = Θ/360∙πr 2 Area: K = ½ r 2 Θ K = ½rs A sector has a perimeter of 16 cm and an area of 15 cm 2. Find its radius and arclength.

An objects apparent size is the angle that is formed by a line of sight to the top and bottom of the object.

Jupiter has an apparent size of.01 o when it is 8 x 10 8 km from the earth. Find the diameter of Jupiter.

assignment Page 264 Problems 2-14 even, 15,18,19,21,22, 20ec