1. Measurement of Rotation
Section 2.2
Measurement of Rotation

2. An angle is in standard position in a Cartesian coordinate system if
Definition: Standard Position of an Angle
An angle is in standard position in a Cartesian coordinate system if
Its vertex is at the origin
Its initial side is along the positive horizontal axis
It is measured counterclockwise from the horizontal axis if the angle measure is positive and clockwise from the horizontal axis if the angle measure is negative
Note: We will be using a u-v coordinate system instead of x-y

3. Definition: Coterminal Angles
Two angles in standard position are coterminal if and only if their degree measures differ by a multiple of 360 degrees. That is
and
are coterminal if and only if
where n stands for an integer.
Note: coterminal angles have terminal sides that coincide, hence the name

4. Definition: Reference Angle
The reference angle of an angle in standard position is the positive, acute angle between the horizontal axis and the terminal side.
Note: Reference angles are always measured counterclockwise. Angles whose terminal sides fall on one of the axes do not have reference angles.

5. 1
What is the reference angle measurement for an angle of 71 degrees in standard position?

6. 2
What is the reference angle measurement for an angle of 133 degrees in standard position?

7. 3
What is the reference angle measurement for an angle of 254 degrees in standard position?

8. 4
What is the reference angle measurement for an angle of 317 degrees in standard position?

9. Example 2
Sketch an angle of in standard position, and determine a coterminal angle between 0 and 360 degrees.

10. 5
What is the reference angle for an angle of 4897 degrees in standard position?