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Section 5-1. Angle and Degree Measure. 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.

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Section 5 1

Section 5-1

Angle and Degree Measure


Vocabulary
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



Angles and degree measure
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?



Write each measure as a decimal to the nearest thousandth
Write each measure as a decimal to the nearest thousandth.

  • 144° 12’ 30”

    2. -107° 12’ 45”


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


Quadrantal angle
Quadrantal Angle

How many degrees in one full rotation around the coordinate system?



Give the angle measure represented by each rotation
Give the angle measure represented by each rotation.

1. 9.5 rotations clockwise.

2. 6.75 rotations counter clockwise.


Coterminal angles
Coterminal Angles


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°


Reference angles
Reference Angles

A 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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