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Pre-Calc tues 10/14 Goals 1. Calculate the area and arc length of a sector 2. Use arc length to estimate the size of distant objects. Problem solving We used a problem solving strategy to lead us to the idea of apparent size, and knowledge of when we might use it. Problem solving from the beginning What question do you want to answer? What do you need to answer it? Answer the question. Does you answer make sense? Arc length The arc length of a sector, s, is given by the formula 𝑠 = 𝑟𝜃, when theta is given in radians. 𝑠 = 𝜃 360 ∗ 2𝜋𝑟, when theta is given in degrees Area of a sector The area of a sector, K, is: 1 2 𝐾 = 𝑟 2 𝜃, when theta is given in radians 𝐾 = 𝜃 360 ∗ 𝜋𝑟 2 , when theta is in degrees Apparent size The apparent size is the angle an object subtends with your eye, when viewed from a distance. The height or diameter of an object can be estimated using arc length, with apparent size as the central angle of the sector. Distance from the observer to the object is the radius of the sector. For small central angles the approximation is quite close. For more information Talk to your peers who were in class. See your text book: read section 7-2, pg 263 We did the class exercises in class. Homework Pg. 265, written exercises 1-21 odd, plus #16