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Arc length and area of a sector

Arc length and area of a sector. Trigonometry - Honors. CLOSURE:. Think of another real-world application for arc length and area of a sector…. WARM-UP: . Three pizzas of the given diameter are cut as indicated. Which cut produces the largest pieces?

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Arc length and area of a sector

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  1. Arc length and area of a sector Trigonometry - Honors

  2. CLOSURE: • Think of another real-world application for arc length and area of a sector…

  3. WARM-UP: • Three pizzas of the given diameter are cut as indicated. Which cut produces the largest pieces? • An 8-inch pizza cut into 6 congruent slices. • A 12-inch pizza cut into 8 congruent slices. • A 16-inch pizza cut into 10 congruent slices.

  4. Pg 475 #85-90 HW Answers 85) 89) 86) 90) 87) 88)

  5. Arc length: • What is the formula for Circumference? • What if we just wanted a chunk of the circumference? This is called arc length.

  6. Find the arc length… • https://www.khanacademy.org/math/trigonometry/basic-trigonometry/radians_tutorial/v/radian-measure-and-arc-length#! • Example 1:

  7. Find the arc length… • EXAMPLE 2: • EXAMPLE 3: Find the measure of the angle in radians and degrees…

  8. Real-world examples… 1) Find the distance traveled in one back and forth swing by the weight of a 16 inch pendulum that swings through a 70 degree angle… note: the angle indicated below is half of the swing.

  9. Real-world examples… 2) The chain of a bicycle travels along the front and rear sprockets, as shown. The circumference of each sprocket is given. • Circumference of rear sprocket = 12 inches. • Circumference of front sprocket = 20 inches • A) About how long is the chain? • B) On the chain, the teeth are spaced in ½ inch intervals. About how many teeth are there on this chain? 10 inches 185 degrees 16o degrees 10 inches

  10. Area of a sector… Pie are not square! Pie are round! What is the formula for the Area of a circle? Suppose you just wanted a chunk of the circle. This is called a sector. Here is the formula for Area of a Sector…

  11. Quick vocab check!

  12. AREA OF A SECTOR… 1) 2)

  13. Finding the area of a segment of a circle… • Problem:Find the area of a segment of a circle with a central angle of 120 degrees and a radius of 8  Express answer to nearest integer.

  14. Segment solution… • Solution:Start by finding the area of the sector: • Now, find the area of the triangle.  Dropping the altitude forms a 30-60-90 degree triangle.  Using trig. (or the 30-60-90 rules), find the altitude, which is 4, and the other leg, which is 4√3 ≈6.93.

  15. Real-world application… • A stretched out paper fan forms a sector with a radius of 18 cm and an angle of 175⁰. Calculate the area of the stretched out fan using the formula A = x/360 × π × r². Give your answer to the nearest tenth. • A = 175/360 × π × 18² ≈494.8 cm²

  16. Real-world application… • A window wiper of length 20 inches goes through an angle of 160⁰. Work out the area of window covered by the window wiper. • The area of screen covered by the wiper makes a sector with a radius of 20 inches and inside angle 160⁰. The first 4 inches of the windshield wiper do not actually remove any water, but simply hold the blade. What is the area covered by the windshield wipers? What is the area of the windshield that water is being removed from? Answer: 536.2 square inches ----20 inches---- --4 in--

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