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Angles and Their Measure

Angles and Their Measure. Section 3.1. 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.

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Angles and Their Measure

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  1. Angles and Their Measure Section 3.1

  2. 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.

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

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

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

  6. 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

  7. 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

  8. 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

  9. Convert from Degrees to Radians and from Radians to Degrees • Degrees to radians Multiply by • Radians to degrees Multiply by

  10. Convert to radians 60° -150° 107°

  11. Convert to degrees 3 radians

  12. Memorize the table on page 121

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

  14. 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°

  15. Find the Linear Speed of an Object Traveling in Circular Motion Linear Speed Angular Speed

  16. Page 126 #97

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

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