Math Study Strategies
Radians and Degrees
Definitions
For more information about this and other math topics, come to the Math Lab 722-6300 x 6232. Caproiu & Hall, 2000. Created by Varaz and Vasag Bozoghlanian.
Radian: the length of the arc of a sector in a circle.
Degree: the measure of the angle between the initial ray and the terminal ray.
Conversions
π
180o
o
To convert radians to degrees, multiply radians by 180
π
To convert degrees to radians, multiply degrees by
Examples
Convert 45° to radians.
Convert
π
to degrees.
6
45o ×
π
45 π π
=
=
o
180
180 4
π 180o 180o
×
=
= 30o
6
π
6
Angles in the Four Quadrants
Quadrant
I
II
III
IV
Associated angle θ
(in degrees)
0 < θ < 90
90 < θ < 180
180 < θ < 270
270 < θ < 360
Associated angle θ
(in radians)
0 < θ < π /2
π /2 < θ < π
π < θ < 3 π /2
3 π /2 < θ < 2 π
Types of Angles
Type of Angle
Acute
Obtuse
Right
Straight
Complementary
Supplementary
Angle's measure
(in degrees)
0 - 90
90 - 180
90
180
α + β = 90
α + β = 180
Angle's measure
(in radians)
0 - π /2
π /2 - π
π /2
π
α + β = π /2
α+β =π
Learning Center
II
I
III
IV