1. ANGLES & ANGLE MEASURES

2. NOTE: Clockwise: Negative Counterclockwise: Positive
TERMINAL SIDE
Clockwise
(Negative)
INITIAL SIDE
Counterclockwise
(Positive)

3. Radian measures are based on a Unit Circle which has a radius of 1.
C (circumference)= 2πr and C = 360˚
2πr = 360˚
2π radians = 360 degrees

4. the positive x-axis and the vertex is at the origin.
Standard Position: An angle is in standard position if the initial side is
the positive x-axis and the vertex is at the origin.
Coterminal Angles: Angles that have the same terminal side, but different
measures (ex: 30˚ and 390˚, which is 360˚ + 30˚…
…they both look alike, but 390˚ has actually gone all
the way around once plus a little farther.)
30˚ angle
390˚ angle

5. Reference Angle: An angle between 0˚ and 90˚
“Back in the day” before calculators were so prevalent, people used trig tables
Which had the sin, cos, and tan for angles between 0˚ & 90˚.
Ex: 300˚ is a 60˚ in Quad. IV, so the reference angle for 300˚ is 60˚.
Ex: -135˚ is a 45˚ in Quad. III, so the reference angle for -135˚ is 45˚.

6. To change from DEGREES to RADIANS:
To change from RADIANS to DEGREES:
Degrees =

7. Ex: 36˚=
Ex:
33.75˚
-1020˚
Ex:
Ex: -820° =