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Understanding General Angle and Radian Measure

Learn how to define general angles and radian measure, determine coterminal angles, convert degrees to radians, and calculate arc length and area of sectors. Includes examples and exercises.

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Understanding General Angle and Radian Measure

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  1. Page 856 13.2 - Define General Angles and Radian Measure

  2. 13.2 - Define General Angles and Radian Measure

  3. Define General Angles and Radian Measure Section13.2 13.2 - Define General Angles and Radian Measure

  4. Definitions • Angle of Rotation is formed by two rays with a common endpoint, also called the vertex. • One ray is called the initial side. • The other ray is called the terminal side. • The measure of the angle is determined by the amount and direction of rotation from the initial side to the terminal side. • Coterminal angles are angles in standard position with the same terminal side • To determine the coterminal angles, add and/or subtract 360° (Magic Number is 360°) • Coterminalangles can be negative • There are an infinite amount of coterminal angles 13.2 - Define General Angles and Radian Measure

  5. Example 1 Draw 210° with the given measure in standard position. Then, determine which quadrant the terminal side lies. • Label the axis when drawing angles • Must draw the angle and its arrow (to indicate both the direction) receive full credit 210° 13.2 - Define General Angles and Radian Measure

  6. Example 2 Draw –45° with the given measure in standard position. Then, determine in which quadrant the terminal side lies. –45° 13.2 - Define General Angles and Radian Measure

  7. Example 3 Draw 510° with the given measure in standard position. Then, determine in which quadrant the terminal side lies. • Get the actual angle 510° - 360° = 150° • So the terminal side makes 1 complete revolution and continues another 150°. 150° 510° 13.2 - Define General Angles and Radian Measure

  8. Your Turn Draw 400° with the given measure in standard position. Then, determine in which quadrant the terminal side lies. 13.2 - Define General Angles and Radian Measure

  9. Example 4 • Find the measures of a positive and negative angles that are coterminal with ө = 40°. Magic Number: 360° 40° 13.2 - Define General Angles and Radian Measure

  10. Example 5 • Find the measures of a positive and negative angles that are coterminal with ө = 65° 13.2 - Define General Angles and Radian Measure

  11. Your Turn • Find the measures of a positive and negative angles that are coterminal with ө = 740° 13.2 - Define General Angles and Radian Measure

  12. Radian Measure • Degree measure is a unit of application such as surveying and navigation • Radian measure is a unit of measure for theoretical work in mathematics. Before angles, they measured in Radian Measure • One radian is the measure of an angle in standard position whose terminal side intercepts an arc of length, r. r r one radian 13.2 - Define General Angles and Radian Measure

  13. Conversions • To convert degrees to radians, multiply π/180° • To convert radians to degrees, multiply 180°/π • 180° = π Radian • 1° = π/180 Radian • 180°/π = 1 Radian 13.2 - Define General Angles and Radian Measure

  14. Example 6 • Convert 240° into radian measure 13.2 - Define General Angles and Radian Measure

  15. Example 7 • Convert –90° into radian measure 13.2 - Define General Angles and Radian Measure

  16. Your Turn • Convert 2° into radian measure 13.2 - Define General Angles and Radian Measure

  17. Example 8 • Convert 9π/2 into degree measure 13.2 - Define General Angles and Radian Measure

  18. Example 9 • Convert 1 Radian into degree measure 13.2 - Define General Angles and Radian Measure

  19. Arc Length and Area of Sector • Sector is a region of the circle that bounded by two radii and an arc of a circle • The Central Angle of a sector is the angle formed by the two radii • Arc Length equation: s = r ө • Area of a Sector: A = (r2ө)/2 • Degrees must be converted to Radians Arc Length, s 13.2 - Define General Angles and Radian Measure

  20. Example 10 • Determine the Arc Length and Area of Sector with the given radius of r = 4 inches and ө = π/6. 13.2 - Define General Angles and Radian Measure

  21. Example 11 • Determine the Arc Length and Area of Sector with the given radius of r = 15 inches and ө = 45°. 13.2 - Define General Angles and Radian Measure

  22. Example 12 • Determine the Arc Length and Area of Sector with the given radius of r = 180 feet and ө = 90°. 13.2 - Define General Angles and Radian Measure

  23. Your Turn • Determine the Arc Length and Area of Sector with the given radius of r = 8 inches and ө = 115°. 13.2 - Define General Angles and Radian Measure

  24. Assignment • Page 862 • 3-37 odd, 33-37 leave π form 13.2 - Define General Angles and Radian Measure

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