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Section 5-1
Angle and Degree Measure
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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
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Angles in Real – World Situations
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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?
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Change each measure to degrees, minutes and seconds.
1. 13.75°
2. 75.72 °
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Write each measure as a decimal to the nearest thousandth.
1. 144° 12’ 30”
2. -107° 12’ 45”
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Quadrantal Angle- An angle where the terminal side coincides with one of the axes.
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Quadrantal Angle
How many degrees in one full rotation around the coordinate system?
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Rotation
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Give the angle measure represented by each rotation.
1. 9.5 rotations clockwise.
2. 6.75 rotations counter clockwise.
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Coterminal Angles
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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.
1. 850°
2. 1012°
3. -65°
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Reference AnglesA reference angle is defined as the acute angle formed by the terminal side of the given angle and the x-axis.
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Find the measure of the reference angle for each angle.
1. 120°
2. -135°