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Angles and Their Measure Section 3.1

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Objectives Convert between degrees, minutes, and seconds (DMS) and decimal forms for angles. Find the arc length of a circle. Convert from degrees to radians, and from radians to degrees. Find the area of a sector of a circle. Find the linear speed of an object traveling in circular motion.

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Background Info Ray Vertex Angle –Initial side –Terminal side Counterclockwise/positive rotation Clockwise/negative rotation Standard position

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Background Info Quadrantal angles/angles that lie in quadrant Measures of rotation: Degrees and Radians

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Draw the following angles: 45°-90° 225°405°

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Converting between DMS & Degrees 1 counterclockwise revolution = 360° 1° = 60’ (60 minutes) 1’ = 60” (60 seconds) Make sure calculator is set in degrees mode Example: Convert 21.256° to DMS: Example: Convert 50°6’21” to a decimal in degrees

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Radians Central angle (θ): angle whose vertex is at the center of a circle Measure of 1 radian: length of radius = arc length Find the arc length (s) of a circle using the following formula: s = rθ Central angle must be in radians in order to use this formula. Example: Page 125 #71

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Convert from Degrees to Radians and from Radians to Degrees Since one revolution is 360°, and the circumference of a circle equals 2πr, then s = rθ 2πr = rθ θ = 2π radians and 1 revolution = 2π radians Therefore, 180° = π radians

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Convert from Degrees to Radians and from Radians to Degrees Degrees to radians Multiply by Radians to degrees Multiply by

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Convert to radians 60° -150° 107°

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Convert to degrees 3 radians

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Memorize the table on page 121

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Pages 124-125 (11-77 odds) Check answers in the back of the book

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Find the Area of a Sector of a Circle Example: Find the area of the sector of a circle of radius 2 feet formed by an angle of 30°

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Find the Linear Speed of an Object Traveling in Circular Motion Linear SpeedAngular Speed

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Page 126 #97

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Pages 125-127 (79-115 odds) Check answers in the back of the book

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Think back to geometry and write down everything you remember about angles.

Think back to geometry and write down everything you remember about angles.

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