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2.1 Angles and Their Measures Warm-up Learning Objective: Students will be able to define and identify angle measures. In doing so, students will identify whether an angle measure is positive or negative based on the direction it is created. The section introduces arc length and provides a formula students will be able to use to find the length. 1. Find the area A and circumference C of a circle with radius 5 meters. 2. Find the area A and circumference C of a circle with radius 2 feet. 3. Approximate the measures of the following angles: a. b. c. d.

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2 rays make an angle Initial side - the first side of an angle, usually on the x-axis Terminal side - the other side - in the counter-clockwise direction of the initial side. Vertex - the point where the rays intersect and if it lies on the origin, the angle is in standard position. **Negative angles go from initial to terminal in a clockwise direction Degrees: 1 full revolution is 360º 1/2 of a revolution is 180º 1/4 of a revolution is 90º 1º is 1/360 of a revolution

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Ex 1 - Draw each Angle a) 45 º b) -90 º c) 225 º d) 405 º e) -150 º

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What happens between degrees?? Degrees (º)>Minutes(‘)>Seconds(“) 1 full rotation = 360º Converting DºM‘S“ to decimal form- Ex 1 - a. Convert 50º6‘21“ to decimal form 50 º º

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b. Convert º to DºM‘S“ form Use the calculator!!

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Arc Length - Central Angle - vertex is at the center of a circle distance around a portion of a circle arc length radius central angle measure MUST be in radians!!! Ex 3: Find the length of the arc of a circle with radius 2m subtended (intersected) by a central angle of 0.25 radians

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HW – p. 124 #1,2,11-16,23-26,29-32,71-74

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