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Understanding Angles and Degree Measure: Vocabulary and Real-World Applications

This section covers essential vocabulary related to angles and degree measurements, including definitions of degree, minute, and second. It also discusses real-world applications, such as the use of a sextant for navigation by measuring the angular elevation of stars to determine latitude. The section guides readers on converting angles to degrees, minutes, and seconds, and finding coterminal and reference angles. The concepts are illustrated with practical examples, enhancing comprehension of angle measures in various scenarios.

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Understanding Angles and Degree Measure: Vocabulary and Real-World Applications

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  1. Section 5-1 Angle and Degree Measure

  2. Vocabulary • Degree - the measure of an angle that is of a complete rotation in the positive direction. • Minute - a unit of angle measure that is one sixtieth of a degree. • Second - a unit of angle measure that is one sixtieth of a minute. • Note – make sure calculator is on degrees

  3. Angles in Real – World Situations

  4. Angles and Degree Measure Navigation – The sextant is an optical instrument invented around 1730. It is used to measure the angular elevation of stars, so that a navigator can determine the ship’s current latitude. Suppose a navigator determines a ship in the Pacific Ocean to be located at north latitude 15.735°. How can this be written as degrees, minutes, and seconds?

  5. Change each measure to degrees, minutes and seconds. • 13.75° 2. 75.72 °

  6. Write each measure as a decimal to the nearest thousandth. • 144° 12’ 30” 2. -107° 12’ 45”

  7. Quadrantal Angle- An angle where the terminal side coincides with one of the axes.

  8. Quadrantal Angle How many degrees in one full rotation around the coordinate system?

  9. Rotation

  10. Give the angle measure represented by each rotation. 1. 9.5 rotations clockwise. 2. 6.75 rotations counter clockwise.

  11. Coterminal Angles

  12. If each angle is in standard position, determine a coterminal angle that is between 0 and 360 degrees. State the quadrant in which the terminal side lies. • 850° • 1012° • -65°

  13. Reference Angles A reference angle is defined as the acute angle formed by the terminal side of the given angle and the x-axis.

  14. Find the measure of the reference angle for each angle. • 120° • -135°

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