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1.1 Angles, Degrees and Arcs

1.1 Angles, Degrees and Arcs. Angles Degree measure of angles Angles and arcs Approximation of Earth’s circumference Approximation of the diameters of the sun and moon. Angles.

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1.1 Angles, Degrees and Arcs

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  1. 1.1 Angles, Degrees and Arcs • Angles • Degree measure of angles • Angles and arcs • Approximation of Earth’s circumference • Approximation of the diameters of the sun and moon

  2. Angles • Degree measure: An angle formed by one complete rotation of the terminal side in a counterclockwise direction has measure 360º. And angle with measure 1º is formed by 1/360 of the complete rotation.

  3. Right Triangle Ratios Special Angles

  4. Angle Measurement • Degrees, minutes and seconds are used to measure angles. 1 degree = 60 minutes 1 degree = 3600 seconds 1 minute = 60 seconds • Convert 12º6’23” to degrees: 6’ = (6/60)º and 23” = (23/3600)º 12º6’23” = (12 + 6/60 + 23/3600)º = 12.106º

  5. Angles and Arcs • The circumference of a circle C, the length of an arc s, and the central angle subtended by the arc qare related by q/ 360º = s / C Eratosthenes’ approximation: 7.5º/360º = 500 mi./C C = 24,000 miles Actual value today: 24, 875 miles

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