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Section 4.1 Notes

Section 4.1 Notes. Angles & Their Measures. Angles and Their Measure. Angles measured in two different “units” Degrees: examples Degrees-Minutes-Seconds = DMS Decimal degrees Radians:. Conversions. Decimal Degrees to DMS. DMS to Decimal Degrees. RADIANS. What is a RADIAN?

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Section 4.1 Notes

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  1. Section 4.1 Notes Angles & Their Measures

  2. Angles and Their Measure • Angles measured in two different “units” • Degrees: examples • Degrees-Minutes-Seconds = DMS • Decimal degrees • Radians:

  3. Conversions Decimal Degrees to DMS DMS to Decimal Degrees

  4. RADIANS What is a RADIAN? A radian is simply another unit of measure for angles. Just as one can measure length in meters or feet, one can measure angles in degrees or radians. A radian is the measure of a central angle that intercepts an arc length equal to that of the circle’s radius. A central angle is the angle formed by two rays with the center of a circle as their common endpoint. Consider the circle with radius, r, shown below: The measure of this angle is 1 RADIAN B Q: How many radians to equal 360 degrees? O A

  5. Conversions with Radians

  6. Calculating Arc Length An arc length is just a portion of the entire circumference. Determine the portion using the angle measure.

  7. Calculating Sector Area A sector area is just a portion of the entire circle’s area. Determine the portion using the angle measure.

  8. Nautical Mile A nautical mile is the length of 1 minute of arc along the earth’s equator. 1 Nautical Mile The diameter of the earth is, on average, 7912.18 “statute” (land) miles. Therefore the radius is ½ (7912.18 ) = 3956 statute miles.

  9. Nautical/Statute Mile Conversion Angle Measure = 1’ 1 Nautical Mile

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