Pre­Calc/Trig A
February 06, 2015
5­1
Angles and Degree
Measure
5­1 Angles & Degree Measure
Pre­Calc/Trig A
February 06, 2015
Parts of an angle:
Terminal Side
Initial Side
Vertex
5­1 Angles & Degree Measure
Pre­Calc/Trig A
February 06, 2015
Standard Position:
an angle with its vertex at the origin and initial side on the positive x­axis
5­1 Angles & Degree Measure
Pre­Calc/Trig A
February 06, 2015
Degree: most common unit for measuring an angle
Degrees, Minutes, Seconds:
a more precise angle measurement
1 degree = 60 minutes
1 minute = 60 seconds
1 degree = _______ seconds
5­1 Angles & Degree Measure
Pre­Calc/Trig A
February 06, 2015
Example: Convert the angle to degrees, minutes, and seconds
1. 329.125°
2. -72.775°
Convert each angle to a decimal, rounded to the nearest
thousandth.
3. -128° 30’ 45”
5­1 Angles & Degree Measure
4. 35° 12’ 17”
Pre­Calc/Trig A
February 06, 2015
Quadrantal Angle:
an angle whose terminal side is on one of the axes
Clockwise Rotation: rotation of ­360º
Counterclockwise Rotation:
rotation of 360º
5­1 Angles & Degree Measure
Pre­Calc/Trig A
February 06, 2015
Example: Give the angle measure represented by each
rotation.
1. 9.5 rotations clockwise
2. 6.75 rotations counterclockwise
5­1 Angles & Degree Measure
Pre­Calc/Trig A
February 06, 2015
Coterminal Angles:
two angles that have the same terminal side when they are in standard position
For any angle, A, coterminal angles can be found using A + 360ºk, where k is an integer
5­1 Angles & Degree Measure
Pre­Calc/Trig A
February 06, 2015
Example: Identify all angles that are coterminal with each
angle. Then find one positive and one negative angle that are
coterminal.
1. 86°
2. 294°
For an angle in standard position, determine a coterminal
angle between 0° and 360°. State the quadrant in which the
terminal side lies.
3. 595°
5­1 Angles & Degree Measure
4. -777°
Pre­Calc/Trig A
February 06, 2015
Reference Angle:
the acute angle formed by the terminal side of the angle and the x­axis.
5­1 Angles & Degree Measure
Pre­Calc/Trig A
February 06, 2015
Example: Find the measure of the reference angle for each
angle.
1. 312°
5­1 Angles & Degree Measure
2. -195°