1. ANGLE MEASURES
PREACALCULUS
LESSON 2 – 1

2. STANDARD POSITION
An angle is in STANDARD POSITION if the vertex is at the origin and the one ray is on the positive x-axis.
120 degrees degrees

3. RADIANS The distance around a circle is 2π.
Radians express the angle as a fraction of that 2π.

4. DRAW AN ANGLE
215 degrees degrees
3π/4 degrees -π/6 degrees

5. CONVERTING FROM DEGREES TO RADIANS
Radians are another way to measure angles and are based on the circumference of the circle.
One π radian = 180 degrees
Two π radians = 360 degrees
To convert degrees to radians, multiply by
To convert radians to degrees, multiply by

6. CONVERT THESE
-30 degrees 5π
120 degrees π

7. COTERMINAL ANGLES
Every rotation around the coordinate plane is 360 degrees or 2π radians.
So to find a coterminal angle, add or subtract 360 or 2π till you have a normal angle.

8. FIND COTERMINAL ANGLES
390 degrees degrees
8π/ π/5

9. DEGREES, MINUTES, SECONDS
To express an angle in a more precise way, you can use minutes and seconds appended to the degrees.
125o 38’ 125”